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    Wyświetlanie 1-69 z 69
    Tytuł:
    Monotonic solutions of multi term fractional differential equations
    Autorzy:
    Salem, Hussein A. H.
    Powiązania:
    https://bibliotekanauki.pl/articles/745873.pdf
    Data publikacji:
    2007
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Fractional calculus
    fixed point theorem
    Cauchy problem
    Opis:
    In this paper, we present an existence of monotonic solutions for a nonlinear multi term non-autonomous fractional differential equation in the Banach space of summable functions. The concept of measure of noncompactness and a fixed point theorem due to \(G\). Emmanuele is the main tool in carring out our proof.
    Źródło:
    Commentationes Mathematicae; 2007, 47, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Continuous solutions of a polynomial-like iterative equation with variable coefficients
    Autorzy:
    Zhang, Weinian
    Baker, John
    Powiązania:
    https://bibliotekanauki.pl/articles/1208028.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    functional equation
    fixed point theorem
    iterative root
    Opis:
    Using the fixed point theorems of Banach and Schauder we discuss the existence, uniqueness and stability of continuous solutions of a polynomial-like iterative equation with variable coefficients.
    Źródło:
    Annales Polonici Mathematici; 2000, 73, 1; 29-36
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the constrained and unconstrained controllability of semilinear Hilfer fractional systems
    Autorzy:
    Sikora, Beata
    Powiązania:
    https://bibliotekanauki.pl/articles/27312002.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    Hilfer fractional derivative
    fractional systems
    semilinear control systems
    nonautonomous systems
    Rothe's fixed point theorem
    generalized Darbo fixed point theorem
    Opis:
    In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function f depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe’s fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study.
    Źródło:
    Archives of Control Sciences; 2023, 33, 1; 155--178
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundary value problems for second order delay differential equations
    Autorzy:
    Skóra, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/254891.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    functional differential equation
    existence
    uniqueness
    fixed point theorem
    Opis:
    We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order.
    Źródło:
    Opuscula Mathematica; 2012, 32, 3; 551-558
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some algebraic fixed point theorems for multi-valued mappings with applications
    Autorzy:
    Dhage, Bupurao
    Powiązania:
    https://bibliotekanauki.pl/articles/729576.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    ordered space
    fixed point theorem and differential inclusion
    Opis:
    In this paper, some algebraic fixed point theorems for multi-valued discontinuous operators on ordered spaces are proved. These theorems improve the earlier fixed point theorems of Dhage (1988, 1991) Dhage and Regan (2002) and Heikkilä and Hu (1993) under weaker conditions. The main fixed point theorems are applied to the first order discontinuous differential inclusions for proving the existence of the solutions under certain monotonicity condition of multi-functions.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2006, 26, 1; 5-55
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of $ \mathbb{R}^n $
    Autorzy:
    Bachar, Imed
    Mâagli, Habib
    Eltayeb, Hassan
    Powiązania:
    https://bibliotekanauki.pl/articles/29519177.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonnegative solution
    semipositone
    Kato class
    fixed point theorem
    Opis:
    In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of $ \mathbb{R}^n $ (n ≥ 2). The global behavior of this solution is also given.
    Źródło:
    Opuscula Mathematica; 2022, 42, 6; 793-803
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On controllability for fractional differential inclusions in Banach spaces
    Autorzy:
    Wang, J.
    Li, X.
    Wei, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/256046.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    controllability
    fractional differential inclusions
    Bohnenblust-Karlin's fixed point theorem
    Opis:
    In this paper, we investigate the controllability for systems governed by fractional differential inclusions in Banach spaces. The techniques rely on fractional calculus, multivalue mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem.
    Źródło:
    Opuscula Mathematica; 2012, 32, 2; 341-356
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multi-valued operators and fixed point theorems in Banach algebras
    Autorzy:
    Dhage, Bapur
    Powiązania:
    https://bibliotekanauki.pl/articles/729606.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    multi-valued operator
    fixed point theorem and integral inclusion
    Opis:
    In this paper, two multi-valued versions of the well-known hybrid fixed point theorem of Dhage [6] in Banach algebras are proved. As an application, an existence theorem for a certain differential inclusion in Banach algebras is also proved under the mixed Lipschitz and compactness type conditions.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 97-122
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multiple positive solutions to singular boundary value problems for superlinear second order FDEs
    Autorzy:
    Jiang, Daqing
    Powiązania:
    https://bibliotekanauki.pl/articles/1207893.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    superlinear
    fixed point theorem
    singular boundary value problem
    existence
    Opis:
    We study the existence of positive solutions to the singular boundary value problem for a second-order FDE

    ⎧ u'' + q(t) f(t,u(w(t))) = 0, for almost all 0 < t < 1,
    ⎨ u(t) = ξ(t), a ≤ t ≤ 0,
    ⎩ u(t) = η(t), 1 ≤ t ≤ b,

    where q(t) may be singular at t = 0 and t = 1, f(t,u) may be superlinear at u = ∞ and singular at u = 0.
    Źródło:
    Annales Polonici Mathematici; 2000, 75, 3; 257-270
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Positive solutions of boundary value problems with nonlinear nonlocal boundary conditions
    Autorzy:
    Padhi, S.
    Pati, S.
    Hota, D. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/255207.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    positive solutions
    Leggett-Williams fixed point theorem
    nonlinear boundary conditions
    Opis:
    We consider the existence of at least three positive solutions of a nonlinear first order problem with a nonlinear nonlocal boundary condition given by [formula] where r : [0,1] → [0, ∞) is continuous; the nonlocal points satisfy [formula] the nonlinear function ƒi and [formula] are continuous mappings from [0,1] x [0,∞) → [0,∞) for i = 1,2,... ,m and j = 1, 2,. .. , n respectively, and λ > 0 is a positive parameter.
    Źródło:
    Opuscula Mathematica; 2016, 36, 1; 69-79
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Quadratic integral equations in reflexive Banach space
    Autorzy:
    Salem, Hussein
    Powiązania:
    https://bibliotekanauki.pl/articles/729287.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Pettis integral
    fractional calculus
    fixed point theorem
    quadratic integral equation
    Opis:
    This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 1; 61-69
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stability analysis of implicit fractional differential equations with anti-periodic integral boundary value problem
    Autorzy:
    Zada, Akbar
    Waheed, Hira
    Powiązania:
    https://bibliotekanauki.pl/articles/1791429.pdf
    Data publikacji:
    2020-01-01
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Implicit fractional differential equations
    Fixed point theorem
    Hyers-Ulam Stability
    Opis:
    In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, and generalized Ulam-Hyers-Rassias stability of the solution to an implicit nonlinear fractional differential equations corresponding to an implicit integral boundary condition. We develop conditions for the existence and uniqueness by using the classical fixed point theorems such as Banach contraction principle and Schaefer's fixed point theorem. For stability, we utilize classical functional analysis. The main results are well illustrated with an example.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2020, 19; 5-25
    2300-133X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bifurcation in a nonlinear steady state system
    Autorzy:
    Wang, G. Q.
    Cheng, S. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/255541.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    bifurcation
    cellular neural network
    steady state
    Krasnoselsky fixed point theorem
    Opis:
    The steady state solutions of a nonlinear digital cellular neural network with ω neural units and a nonnegative variable parameter λ are sought. We show that λ = 1 is a critical value such that the qualitative behavior of our network changes. More specifically, when ω is odd, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ ∈ [1, ∞), steady states cannot exist; while when ω is even, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ = 1, there are no nontrivial steady states, and for λ ∈ (1, ∞), there are two fully oscillatory steady states. Furthermore, the number of existing nontrivial solutions cannot be improved. It is hoped that our results are of interest to digital neural network designers.
    Źródło:
    Opuscula Mathematica; 2010, 30, 3; 349-360
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval
    Autorzy:
    Olszowy, Leszek
    Powiązania:
    https://bibliotekanauki.pl/articles/1912736.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Quadratic Urysohn integral
    measure of noncompactness
    Tichonov fixed point theorem
    Opis:
    We show that \(\omega_0 (X) = \lim_{T\to\infty} \lim_{\varepsilon\to 0} \omega^T (X, \varepsilon)\) is a measure of noncompactness defined on some subsets of the space \(C(\mathbb{R}^+) = \{x\colon \mathbb{R}^+ \to \mathbb{R},\ x\ \text{continuous}\}\) furnished with the distance defined by the family of seminorms \(|x|_n\). Moreover, using a technique associated with the measures of noncompactness, we prove the existence of solutions of a quadratic Urysohn integral equation on an unbounded interval. This measure allows to obtain theorems on the existence of solutions of a integral equations on an unbounded interval under a weaker assumptions then the assumptions of theorems obtained by applying two-component measures of noncompactness.
    Źródło:
    Commentationes Mathematicae; 2008, 48, 1; 103-112
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of nonnegative radial solutions for p-Laplacian elliptic systems
    Autorzy:
    Jiang, Daqing
    Liu, Huizhao
    Powiązania:
    https://bibliotekanauki.pl/articles/1294162.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    elliptic system
    nonnegative radial solution
    existence
    fixed point theorem in cones
    Opis:
    The existence of nonnegative radial solutions for some systems of m (m ≥ 1) quasilinear elliptic equations is proved by a simple application of a fixed point theorem in cones.
    Źródło:
    Annales Polonici Mathematici; 1999, 71, 1; 19-29
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders
    Autorzy:
    Al-Issa, Shorouk
    El-Sayed, Ahmed Mohamed Ahmed
    Powiązania:
    https://bibliotekanauki.pl/articles/746526.pdf
    Data publikacji:
    2009
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    integral inclusion
    fractional-calculus
    Caratheodory condition
    differential inclusion
    fixed point theorem
    Opis:
    In this paper we study the global existence of positive integrable solution for the nonlinear integral inclusion of fractional order \[ x(t) \in p(t) + I^\alpha F_1 (t, I^\beta f_2 (t, x(\varphi(t)))),\quad t \in (0, 1). \] As an application the global existence of the solution for the initial-value problem of the arbitrary (fractional) orders differential inclusion \[ \frac{dx(t)}{dt}\in p(t)+ I^\alphaF_1(t,D^\gammax(t))),\quad \text{a.e.}\ t gt 0 \] will be studied.
    Źródło:
    Commentationes Mathematicae; 2009, 49, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of a fuzzy integral equation of Urysohn-Volterra type
    Autorzy:
    Darwish, Mohamed
    Powiązania:
    https://bibliotekanauki.pl/articles/729473.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fuzzy integral equation
    Urysohn-Volterra
    Hausdorff metric
    Schauder fixed point theorem
    Opis:
    We present an existence theorem for integral equations of Urysohn-Volterra type involving fuzzy set valued mappings. A fixed point theorem due to Schauder is the main tool in our analysis.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 75-82
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Positive solutions with specific asymptotic behavior for a polyharmonic problem on $\mathbb{R}^n$
    Autorzy:
    Dhifli, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1397483.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    asymptotic behavior
    Dirichlet problem
    Schauder fixed point theorem
    positive bounded solutions
    Opis:
    This paper is concerned with positive solutions of the semilinear polyharmonic equation $(-\Delta)^m u = a(x)u^\alpha$ on $\mathbb{R}^n$, where m and n are positive integers with n > 2m, $\alpha \in (—1,1)$. The coefncient a is assumed to satisfy $a(x) \approx (1+|x|)^{-\lambda}L(1+|x|)$ for $ x \in \mathbb{R}^n$, where $ \lambda \in [2m,\infty)$ and $L \in C^1([q,\infty))$ is positive with $ {tL^\prime (t)}/{L(t)} \rightarrow 0 $ as $ t \rightarrow \infty $ if $ \lambda = 2m$, one also assumes that $\int_1^\infty t^{-1} L(t) dt < \infty $. We prove the existence of a positive solution $u$ such that $ u(x) \approx (1 + |x|)^{-\tilde{\lambda}} L(1+|x|)$ for $ x \in \mathbb{R}^n$, with $\tilde{\lambda} := \text{min}(n-2m, {\lambda-2m}/{1-\alpha})$ and a function $ \tilde{L} $, given explicitly in terms of $L$ and satisfying the same condition as infinity. (Given positive functions $f$ and $g$ on $\mathbb{R}^n$, $f \approx g $ means that $c^{-1} g \leq f \leq cg $ for some constant c > 1.)
    Źródło:
    Opuscula Mathematica; 2015, 35, 1; 5-19
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The applications of fixed-point theorem in optimisation problems
    Autorzy:
    Chwastek, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/140506.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    optymalizacja
    histereza
    estymacja parametru
    optimisation
    fixed-point theorem
    hysteresis
    parameter estimation
    Opis:
    The fixed-point theorem is widely used in different engineering applications. The present paper focuses on its applications in optimisation. A Matlab toolbox, chich implements the branch-and-bound optimisation method based on the fixed-point theorem, is used for solving different real-life test problems, including estimation of model parameters for the Jiles-Atherton model.
    Źródło:
    Archives of Electrical Engineering; 2012, 61, 2; 189-198
    1427-4221
    2300-2506
    Pojawia się w:
    Archives of Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the convergence of solutions to second-order neutral difference equations
    Autorzy:
    Migda, Małgorzata
    Migda, Janusz
    Zdanowicz, Małgorzata
    Powiązania:
    https://bibliotekanauki.pl/articles/254721.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    second-order difference equation asymptotic behavior quasi-differences
    Krasnoselskii's fixed point theorem
    Opis:
    A second-order nonlinear neutral difference equation with a quasi-difference is studied. Sufficient conditions are established under which for every real constant there exists a solution of the considered equation convergent to this constant.
    Źródło:
    Opuscula Mathematica; 2019, 39, 1; 61-75
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces
    Autorzy:
    Ezzinbi, Khalil
    Degla, Guy
    Ndambomve, Patrice
    Powiązania:
    https://bibliotekanauki.pl/articles/729519.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    controllability
    integrodifferential equations
    nonlocal initial condition
    resolvent operator
    Mönch fixed-point theorem
    Opis:
    This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and W.S. Li (J. Optim. Theory Appl. 142, 267-273 (2009)), without assuming the compactness of the resolvent operator. An example of application is given for illustration.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 1; 25-46
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solvability of functional quadratic integral equations with perturbation
    Autorzy:
    Metwali, M. A. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/254702.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    quadratic integral equation
    measure of noncompactness
    Krasnoselskii fixed point theorem
    superposition operators
    Opis:
    We study the existence of solutions of the functional quadratic integral equation with a perturbation term in the space of Lebesgue integrable functions on an unbounded interval by using the Krasnoselskii fixed point theory and the measure of weak noncompactness.
    Źródło:
    Opuscula Mathematica; 2013, 33, 4; 725-739
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Right focal boundary value problems for difference equations
    Autorzy:
    Henderson, J.
    Liu, X.
    Lyons, J. W.
    Neugebauer, J. T.
    Powiązania:
    https://bibliotekanauki.pl/articles/255580.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    difference equation
    boundary value problem
    right focal
    fixed point theorem
    positive solution
    Opis:
    An application is made of a new Avery et al. fixed point theorem of compression and expansion functional type in the spirit of the original fixed point work of Leggett and Williams, to obtain positive solutions of the second order right focal discrete boundary value problem. In the application of the fixed point theorem, neither the entire lower nor entire upper boundary is required to be mapped inward or outward. A nontrivial example is also provided.
    Źródło:
    Opuscula Mathematica; 2010, 30, 4; 447-456
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Monotonic solutions for quadratic integral equations
    Autorzy:
    Cichoń, Mieczysław
    Metwali, Mohamed
    Powiązania:
    https://bibliotekanauki.pl/articles/729338.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    integral equation
    monotonic solution
    measure of noncompactness
    Darbo fixed point theorem
    superposition operator
    Opis:
    Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 2; 157-171
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of positive solutions for a fractional boundary value problem with lower-order fractional derivative dependence on the half-line
    Autorzy:
    Boucenna, Amina
    Moussaoui, Toufik
    Powiązania:
    https://bibliotekanauki.pl/articles/729493.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fractional differential equation
    half-line
    Krasnoselsk'ii's fixed point theorem
    existence
    positive solution
    Opis:
    The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 2; 169-189
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the mixed problem for quasilinear partial functional differential equations with unbounded delay
    Autorzy:
    Człapiński, Tomasz
    Powiązania:
    https://bibliotekanauki.pl/articles/1294042.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Carathéodory solutions
    functional differential equation
    bicharacteristics
    fixed-point theorem
    mixed problem
    unbounded delay
    Opis:
    We consider the mixed problem for the quasilinear partial functional differential equation with unbounded delay $D_tz(t,x) = ∑_{i=1}^n f_i(t,x,z_{(t,x)})D_{x_i}z(t,x) + h(t,x,z_{(t,x)})$, where $z_{(t,x)} ∈ X̶_0$ is defined by $z_{(t,x)}(τ,s) = z(t+τ,x+s)$, $(τ,s) ∈ (-∞,0]×[0,r]$, and the phase space $X̶_0$ satisfies suitable axioms. Using the method of bicharacteristics and the fixed-point method we prove a theorem on the local existence and uniqueness of Carathéodory solutions of the mixed problem.
    Źródło:
    Annales Polonici Mathematici; 1999, 72, 1; 87-98
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and attractivity results for nonlinear first order random differential equations
    Autorzy:
    Dhage, B. C.
    Ntouyas, S. K
    Powiązania:
    https://bibliotekanauki.pl/articles/255550.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    random differential equations
    locally attractive
    globally attractive
    local asymptotic attractive
    fixed point theorem
    Opis:
    In this paper, the existence and attractivity results are proved for nonlinear first order ordinary random differential equations. Two examples are provided to demonstrate the realization of the abstract developed theory.
    Źródło:
    Opuscula Mathematica; 2010, 30, 4; 411-429
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of periodic positive solutions to nonlinear Lotka-Volterra competition
    Autorzy:
    Benhadri, Mimia
    Caraballo, Tomas
    Zeghdoudi, Halim
    Powiązania:
    https://bibliotekanauki.pl/articles/255717.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Krasnoselskii's fixed point theorem
    positive periodic solutions
    Lotka-Volterra competition systems
    variable delays
    Opis:
    We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, On positive periodic solution of Lotka-Volterra competition systems with deviating arguments, Proc. Amer. Math. Soc. 134 (2006), 2967-2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature.
    Źródło:
    Opuscula Mathematica; 2020, 40, 3; 341-360
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
    Autorzy:
    Dou, X.
    Li, Y.
    Liu, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255738.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    four-point boundary value problem
    Riemann-Liouville fractional derivative
    Green's functions
    Schauder fixed point theorem
    Opis:
    In this paper, we discuss a four-point boundary value problem for a nonlinear differential equation of fractional order. The differential operator is the Riemann-Liouville derivative and the inhomogeneous term depends on the fractional derivative of lower order. We obtain the existence of at least one solution for the problem by using the Schauder fixed-point theorem. Our analysis relies on the reduction of the problem considered to the equivalent Fredholm integral equation.
    Źródło:
    Opuscula Mathematica; 2011, 31, 3; 359-372
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Picard problem for hyperbolic differential equations in Banach spaces
    Autorzy:
    Sadowski, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/729487.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    boundary value problem
    fixed point theorem
    functional-integral equation
    hyperbolic equation
    measure of noncompactness
    Opis:
    B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation $z_{xy} = f(x,y,z,z_{xy})$ on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation $z_{xy} = f(x,y,z,z_x,z_{xy})$ using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2003, 23, 1; 31-37
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The existence of consensus of a leader-following problem with Caputo fractional derivative
    Autorzy:
    Schmeidel, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/254771.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    leader-following problem
    Caputo fractional differential equation
    consensus, nonlinear system Schauder fixed point theorem
    Opis:
    n this paper, consensus of a leader-following problem is investigated. The leader-following problem describes a dynamics of the leader and a number of agents. The trajectory of the leader is given. The dynamics of each agent depends on the leader trajectory and others agents' inputs. Here, the leader-following problem is modelled by a system of nonlinear equations with Caputo fractional derivative, which can be rewritten as a system of Volterra equations. The main tools in the investigation are the properties of the resolvent kernel corresponding to the Volterra equations, and Schauder fixed point theorem. By study of the existence of an asymptotically stable solution of a suitable Volterra system, the sufficient conditions for consensus of the leader-following problem are obtained.
    Źródło:
    Opuscula Mathematica; 2019, 39, 1; 77-89
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of positive continuous solutions for some polyharmonic elliptic systems on the half space
    Autorzy:
    Zine El Abidine, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/255368.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    polyharmonic elliptic system
    Green function
    Kato class
    positive continuous solution
    Schauder fixed point theorem
    Opis:
    We study the existence of positive continuous solutions of the nonlinear polyharmonic system (-Δ)mu + λqg(v) = 0, (-Δ)mv + μpf(u) = 0 in the half space [formula] where m ≥1 and n>2m.The nonlinear term is required to satisfy some conditions related to the Kato class [formula]. Our arguments are based on potential theory tools associated to (-Δ)m and properties of functions belonging to [formula].
    Źródło:
    Opuscula Mathematica; 2012, 32, 1; 91-113
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces
    Autorzy:
    Yang, Y.
    Wang, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/256027.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    integrodifferential equations
    nonlocal initial condition
    completely continuous operator
    Schaefer fixed point theorem
    mild solution
    Opis:
    In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration.
    Źródło:
    Opuscula Mathematica; 2011, 31, 3; 443-455
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Radial solutions for nonlinear elliptic equation with nonlinear nonlocal boundary conditions
    Autorzy:
    Kossowski, Igor
    Powiązania:
    https://bibliotekanauki.pl/articles/29519502.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonlocal boundary value problem
    radial solution
    elliptic equation
    Krasnoselskii's fixed point theorem in cone
    Opis:
    In this article, we prove existence of radial solutions for a nonlinear elliptic equation with nonlinear nonlocal boundary conditions. Our method is based on some fixed point theorem in a cone.
    Źródło:
    Opuscula Mathematica; 2023, 43, 5; 675-687
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of nonlinear implicit fractional integrodifferential systems
    Autorzy:
    Balachandran, K.
    Divya, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/329784.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    controllability
    fractional derivative
    integrodifferential equations
    fixed point theorem
    sterowalność
    pochodna ułamkowa
    równanie różniczkowe
    punkty stałe
    Opis:
    In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo’s fixed point theorem. Examples are included to verify the result.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 713-722
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results for mild solutions of impulsive periodic systems
    Autorzy:
    Yang, Y.
    Wang, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/254901.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    impulsive periodic systems
    T0-periodic PC-mild solution
    Horn’s fixed point theorem
    existence
    Opis:
    By applying the Horn's fixed point theorem, we prove the existence of T0-periodic PC-mild solution of impulsive periodic systems when PC-mild solutions are ultimate bounded.
    Źródło:
    Opuscula Mathematica; 2012, 32, 3; 601-616
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems
    Autorzy:
    Zeddini, Noureddine
    Sari, Rehab Saeed
    Powiązania:
    https://bibliotekanauki.pl/articles/2216186.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Green function
    Kato class
    nonlinear elliptic systems
    positive solution
    maximum principle
    Schauder fixed point theorem
    Opis:
    Let D be a bounded $C^(1,1)$ -domain in $R^d$, d ≥ 2. The aim of this article is twofold. The first goal is to give a new characterization of the Kato class of functions $K(D)$ that was defined by $N$. Zeddini for $d = 2$ and by $H$. Mâagli and M. Zribi for $d ≥ 3$ and adapted to study some nonlinear elliptic problems in $D$. The second goal is to prove the existence of positive continuous weak solutions, having the global behavior of the associated homogeneous problem, for sufficiently small values of the nonnegative constants $λ$ and $μ$ to the following system $Δu = λf(x, u, v)$, $Δv = μg(x, u, v)$ in D, $u = ϕ_1$ and $v = ϕ_2$ on $∂D$, where $ϕ_1$ and $ϕ_2$ are nontrivial nonnegative continuous functions on $∂D$. The functions $f$ and g are nonnegative and belong to a class of functions containing in particular all functions of the type $f(x, u, v) = p(x)u^(α) h_1 (v)$ and $g(x, u, v) = q(x)h_2 (u)v^β$ with $α ≥ 1$, $β ≥ 1$, $h_1$, $h_2$ are continuous on $[0,∞)$ and $p$, $q$ are nonnegative functions in $K(D)$.
    Źródło:
    Opuscula Mathematica; 2022, 42, 3; 489-519
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solvability of a Quadratic Integral Equation of Fredholm Type Via a Modified Argument
    Autorzy:
    Dal, İlyas
    Temizer, Ӧmer Faruk
    Powiązania:
    https://bibliotekanauki.pl/articles/1818652.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    Fredholm equation
    Hölder condition
    Schauder fixed point theorem
    równanie Fredholma
    nierówność Höldera
    punkt stały Schaudera
    Opis:
    This article concerns with the existence of solutions of thea quadratic integral equation of Fredholm type with a modified argument, \[ x(t) = p(t) + (Fx) (t) \int_{0}^{1} k(t,\tau)x(q(\tau))d\tau \] ,where p, k are functions and F is an operator satisfying the given conditions. Using the properties of the Hölder spaces and the classical Schauder fixed point theorem, we obtain the existence of solutions of the equationunder certain assumptions. Also, we present two concrete examples in which our result can be applied.
    Źródło:
    Journal of Mathematics and Applications; 2020, 43; 47--66
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bounded, asymptotically stable, and L1 solutions of caputo fractional differential equations
    Autorzy:
    Islam, M.N.
    Powiązania:
    https://bibliotekanauki.pl/articles/255179.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Caputo fractional differential equations
    Volterra integral equations
    weakly singular kernel
    Schauder fixed point theorem
    Liapunov's method
    Opis:
    The existence of bounded solutions, asymptotically stable solutions, and L1 solutions of a Caputo fractional differential equation has been studied in this paper. The results are obtained from an equivalent Volterra integral equation which is derived by inverting the fractional differential equation. The kernel function of this integral equation is weakly singular and hence the standard techniques that are normally applied on Volterra integral equations do not apply here. This hurdle is overcomed using a resolvent equation and then applying some known properties of the resolvent. In the analysis Schauder's fixed point theorem and Liapunov's method have been employed. The existence of bounded solutions are obtained employing Schauder's theorem, and then it is shown that these solutions are asymptotically stable by a definition found in [C. Avramescu, C. Vladimirescu, On the existence of asymptotically stable solution of certain integral equations, Nonlinear Anal. 66 (2007), 472-483]. Finally, the L1 properties of solutions are obtained using Liapunov's method
    Źródło:
    Opuscula Mathematica; 2015, 35, 2; 181-190
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space
    Autorzy:
    Almalahi, Mohammed A.
    Panchal, Satish K.
    Powiązania:
    https://bibliotekanauki.pl/articles/1797178.pdf
    Data publikacji:
    2020-07-20
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    ψ-Hilfer fractional derivative
    Mönch fixed point theorem
    Eα-Ulam-Hyers stability
    δ-approximate solution
    Opis:
    In this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss $E_{α}$-Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2020, 19; 171-192
    2300-133X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and Uniqueness of Time Periodic Solution to the Viscous Modified Degasperis-Procesi Equation
    Autorzy:
    Asaduzzaman, Md.
    Ali, Md. Zulfikar
    Powiązania:
    https://bibliotekanauki.pl/articles/1031446.pdf
    Data publikacji:
    2020
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Galerkin’s method
    Leray-Schauder fixed point theorem
    time periodic solution
    viscous modified Degasperis-Procesi equation
    Opis:
    In this paper, we establish the existence and uniqueness criteria of time periodic solution to the viscous modified Degasperis-Procesi (vmDP for short) equation with periodic boundary value conditions. The analysis of this study is based on Galerkin’s method and Leray-Schauder fixed point theorem. Using Galerkin’s method some uniform priori estimates of approximate solution to the corresponding equation of vmDP has been constructed. Furthermore, the efficient and straightforward existence and uniqueness criteria of time periodic solution to the vmDP with periodic boundary value conditions has been obtained.
    Źródło:
    World Scientific News; 2020, 142; 25-43
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a mixed-type integral equation and fractional-order functional differential equations
    Autorzy:
    El-Sayed, A. M. A.
    Sherif, Nagwa
    Ibrahim, I. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/745693.pdf
    Data publikacji:
    2005
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Nonlinear functional integral equation
    fractional calculus
    Volterra operator
    mixed type integral equation
    Schauder fixed point theorem
    Opis:
    In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval \([0, 1]\).
    Źródło:
    Commentationes Mathematicae; 2005, 45, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of time varying semilinear non-instantaneous impulsive systems with delay, and nonlocal conditions
    Autorzy:
    Cabada, Dalia
    Garcia, Katherine
    Guevara, Cristi
    Leiva, Hugo
    Powiązania:
    https://bibliotekanauki.pl/articles/2134894.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    exact controllability
    semilinear time varying control systems
    non-instantaneous impulses
    delay
    nonlocal conditions
    Rothe's fixed point theorem
    Opis:
    In this paper we prove the exact controllability of a time varying semilinear system considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously. It is done by using the Rothe’s fixed point theorem together with some sub-linear conditions on the nonlinear term, the impulsive functions, and the function describing the nonlocal conditions. Furthermore, a control steering the semilinear system from an initial state to a final state is exhibited.
    Źródło:
    Archives of Control Sciences; 2022, 32, 2; 335--357
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Schauders fixed-point theorem in nonlinear controllability problems
    Autorzy:
    Klamka, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/206701.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nieliniowy system sterowania
    sterowalność
    twierdzenie o punkcie stałym
    continuous-time systems
    controllability
    fixed-point theorems
    nonlinear control systems
    Schauder's fixed point theorem
    Opis:
    This paper refers to application of the Schauder's fixed point theorem together with linear controllability results in getting the sufficient controllability conditions for various kinds of controllability and for different types of nonlinear control systems. The following nonlinear control systems are considered : finite-dimensional systems, systems with delays in control or in the state variables, and infinite-dimensional systems. The paper presents the review of results existing in the literature which show how Schauder's fixed-point theorem can be practically used to solve several controllability problems for different types of nonlinear control systems.
    Źródło:
    Control and Cybernetics; 2000, 29, 1; 153-165
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions
    Autorzy:
    Wang, J.
    Yan, X.
    Zhang, X. H.
    Wang, T. M
    Li, X. Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/255673.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    integrodifferential equations
    fractional derivative
    nonlocal conditions
    resolvent operator and their norm continuity
    fixed point theorem
    mild solutions
    Opis:
    In this paper, we discuss a class of integrodifferential equations with nonlocal conditions via a fractional derivative of the type: [formula]. Some sufficient conditions for the existence of mild solutions for the above system are given. The main tools are the resolvent operators and fixed point theorems due to Banach's fixed point theorem, Krasnoselskii's fixed point theorem and Schaefer's fixed point theorem. At last, an example is given for demonstration.
    Źródło:
    Opuscula Mathematica; 2011, 31, 1; 119-135
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions
    Autorzy:
    Zada, Akbar
    Yar, Muhammad
    Li, Tongxing
    Powiązania:
    https://bibliotekanauki.pl/articles/744661.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Caputo fractional derivative
    Riemann–Liouville fractional integral
    coupled system
    existence
    uniqueness
    fixed point theorem
    Hyers–Ulam stability
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2018, 17
    2300-133X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lossless transmission lines terminated by crystal oscillator circuit
    Autorzy:
    Angelov, Vasil G.
    Powiązania:
    https://bibliotekanauki.pl/articles/1065397.pdf
    Data publikacji:
    2019
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Fixed point theorem
    Kirchhoff’s law
    Lossless transmission line
    Mixed problem for hyperbolic system
    Neutral equation
    Periodic solution
    Opis:
    The present paper deals with ТЕМ propagation of waves along lossless transmission lines terminated by a crystal oscillator circuit. The crystal oscillator circuit generates nonlinear boundary conditions derived by the Kirchhoff’s law. Then the mixed problem for the hyperbolic transmission line system to an initial value problem for neutral system on the boundary is reduced. The main purpose of the present paper is to show an existence-uniqueness of a periodic solution of the neutral system. This is achieved by introducing a suitable operator acting on a space of periodic functions. Its fixed point is a periodic solution of the neutral system. The advantages of the presented method on numerical example are demonstrated. The solution can be obtained by successive approximations.
    Źródło:
    World Scientific News; 2019, 132; 65-83
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional nonlocal integrodifferential equations of mixed type with time-varying generating operators and optimal control
    Autorzy:
    Wang, J.
    Wei, W.
    Yang, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/254750.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fractional integrodifferential equations of mixed type
    time-varying generating operators
    nonlocal conditions
    fixed point theorem
    existence
    optimal control
    Opis:
    In this paper, a class of fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is considered. Using a contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequailty, the existence and uniqueness of mild solution are given. The existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is also presented.
    Źródło:
    Opuscula Mathematica; 2010, 30, 2; 217-234
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multiple solutions to third-order differential equations with derivative dependence and deviating arguments
    Autorzy:
    Jankowski, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/1938599.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Gdańska
    Tematy:
    boundary value problems with deviating arguments
    Stieltjes integral boundary conditions
    cone
    existence of positive solutions
    fixed point theorem
    Opis:
    In this paper, we give some new results for multiplicity of positive (nonnegative) solutions for third-order differential equations with derivative dependence, deviating arguments and Stieltjes integral boundary conditions. We discuss our problem with advanced argument α and arbitrary β ∈ C([0,1],[0,1]), see problem (2). It means that argument β can change the character on [0,1], so β can be delayed in some set J¯⊂ [0,1] and advanced in [0,1] \ J¯. Four examples illustrate the main results.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2016, 20, 1; 85-98
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The controllability of nonlinear implicit fractional delay dynamical systems
    Autorzy:
    Joice Nirmala, R.
    Balachandran, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/331001.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    controllability
    fractional delay
    differential equation
    Mittag-Leffler function
    fixed point theorem
    sterowalność
    opóźnienie ułamkowe
    równanie różniczkowe
    funkcja Mittag-Lefflera
    Opis:
    This paper is concerned with the controllability of nonlinear fractional delay dynamical systems with implicit fractional derivatives for multiple delays and distributed delays in control variables. Sufficient conditions are obtained by using the Darbo fixed point theorem. Further, examples are given to illustrate the theory.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 501-513
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllability of nonlinear stochastic systems with multiple time-varying delays in control
    Autorzy:
    Karthikeyan, S.
    Balachandran, K.
    Sathya, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/330584.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    relative controllability
    stochastic control system
    multiple delays in control
    Banach fixed point theorem
    układ sterowania stochastyczny
    twierdzenie Banacha o kontrakcji
    Opis:
    This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2015, 25, 2; 207-215
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The existence of monotonic solutions of a class of quadratic integral equations of Volterra type
    Autorzy:
    Karakurt, Osman
    Temizer, Ӧmer Faruk
    Powiązania:
    https://bibliotekanauki.pl/articles/357726.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    nonlinear Volterra integral equations
    measure of noncompactness
    fixed point theorem
    nieliniowe równania całkowe Volterry
    miara braku zgodności
    twierdzenie o punkcie stałym
    Opis:
    Using the technique associated with measure of noncompactness we prove the existence of monotonic solutions of a class of quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.
    Źródło:
    Journal of Mathematics and Applications; 2019, 42; 117-133
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a cubic integral equation of Urysohn type with linear perturbation of second kind
    Autorzy:
    Awad, H. K.
    Darwish, M. A.
    Metwali, M. M. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/2052410.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    cubic integral equation
    Darbo's fixed point theorem
    monotonicity
    measure of noncompactness
    równanie całkowe
    twierdzenie Darbo o punkcie stałym
    monotoniczność
    miara braku zgodności
    Opis:
    In this paper, we concern by a very general cubic integral equation and we prove that this equation has a solution in C[0; 1]. We apply the measure of noncompactness introduced by Banaś and Olszowy and Darbo's fixed point theorem to establish the proof of our main result.
    Źródło:
    Journal of Mathematics and Applications; 2018, 41; 29-38
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonincreasing solutions for quadratic integral equations of Convolution type
    Autorzy:
    El-Sayed, W. G.
    Abd El-Mowla, A. A. H.
    Powiązania:
    https://bibliotekanauki.pl/articles/357742.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    quadratic integral equation
    measure of noncompactness
    fixed-point theorem
    monotonic solutions
    równanie całkowe
    miara braku zgodności
    twierdzenie o punkcie stałym
    rozwiązania monotoniczne
    Opis:
    We study a nonlinear quadratic integral equation of Convolution type in the Banach space of real functions defined and continuous on a bounded and closed interval. By using a suitable measure of noncompactness, we show that the integral equation has monotonic solutions.
    Źródło:
    Journal of Mathematics and Applications; 2019, 42; 95-107
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the solutions of a class of nonlinear functional integral quations in space C [0,a]
    Autorzy:
    Özdemir, İ.
    Çakan, Ü.
    Powiązania:
    https://bibliotekanauki.pl/articles/357700.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    nonlinear integral equation
    measure of noncompactness
    Darbo fixed point theorem
    Darbo condition
    równanie całkowe
    teoria punktu stałego
    miara niezwartości
    twierdzenie Darboux'a
    własność Darboux
    Opis:
    The principal aim of this paper is to give sufficient conditions for solvability of a class of some nonlinear functional integral equations in the space of continuous functions defined on interval [0,a]. The main tool used in our study is associated with the technique of measures of noncompactness. We give also some examples satisfying the conditions of our main theorem but not satisfying the conditions in [8].
    Źródło:
    Journal of Mathematics and Applications; 2015, 38; 105-114
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximate controllability of the impulsive semilinear heat equation
    Autorzy:
    Leiva, H.
    Merentes, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/357798.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    impulsive semilinear heat equation
    approximate controllability
    Rothe's fixed point theorem
    functional analysis
    teoria punktu stałego
    przestrzeń Banacha
    równanie przewodnictwa ciepła
    sterowalność
    analiza funkcjonalna
    Opis:
    In this paper we apply Rothe's Fixed Point Theorem to prove the interior approximate controllability of the following semilinear impulsive Heat Equation \[ \begin{cases} z_{t} = \Delta z + 1_{\omega}u(t,x) + f(t,z,u(t,x)), & \text{in} \quad (0,\tau] \times \Omega, t \neq t_{k}) \\ z = 0, & \text{on} \quad (0, \tau) \times \delta\Omega,\\ z(0,x) = z_{0}(x), & x \in \Omega, \\ z(t_{k}^{+}, x) = z(t_{k}^{-}, x) + I_{k}(t_{k},z(t_{k},x)u(t_{k},x)), & x \in \Omega, \end{cases} \] where k = 1, 2, . . . , p, $\Omega$ is a bounded domain in $\mathbb{R}^{N}(N \geq 1), z_{0} \in L_{2}(\Omega), \omega$ is an open nonempty subset of $\Omega$, $1_{\omega}$ denotes the characteristic function of the set $\omega$, the distributed control $u$ belongs to $C\left([0, \tau]; L_{2}\left(\Omega\right)\right)$ and $f,I_{k} \in C([0, \tau] \times \mathbb{R} \times \mathbb{R}; \mathbb{R}), k = 1, 2, 3, \ldots, p$, such that \[ |f(t,z,u)| \leq a_{0}|z|^{\alpha_{0}} + b_{0}|u|^{\beta_{0}} +c_{0}, \quad u \in \mathbb{R}, z \in \mathbb{R}. \] \[ |I_{k}(t,z,u)| \leq a_{k}|z|^{\alpha_{k}} + b_{k}|u|^{\beta_{k}} +c_{k}, k=1,2,3 \ldots, pu \in \mathbb{R}, z \in \mathbb{R} \] with $\frac{1}{2} \leq \alpha_{k} < 1, \frac{1}{2} \leq \beta_{k} < 1, k= 0,1,2,3, \ldots, p$ Under this condition we prove the following statement: For all open nonempty subsets $\omega$ of $\Omega$ the system is approximately controllable on $[0, \tau]$. Moreover, we could exhibit a sequence of controls steering the nonlinear system from an initial state $z_{0}$ to an $\epsilon$ neighborhood of the nal state $z_{1}$ at time $\tau > 0$.
    Źródło:
    Journal of Mathematics and Applications; 2015, 38; 85-104
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some qualitative properties of integrable solutions for Cauchy-type problem of fractional order
    Autorzy:
    Metwali, M. M. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/357698.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    Cauchy problem
    Darbo fixed point theorem
    quadratic integral equations
    measure of noncompactness
    problem Cauchy'ego
    twierdzenie o punkcie stałym
    twierdzenie Darbo
    równania całkowe
    miara niezwartości
    Opis:
    The paper discusses the existence of solutions for Cauchy-type problem of fractional order in the space of Lebesgue integrable functions on bounded interval. Some qualitative properties of solutions are presented such as monotonicity, uniqueness and continuous dependence on the initial data. The main tools used are measure of weak (strong) noncompactness, Darbo fixed point theorem and fractional calculus.
    Źródło:
    Journal of Mathematics and Applications; 2017, 40; 121-p134
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Existence of Continuous Positive Monotonic Solutions of a Self-Reference Quadratic Integral Equation
    Autorzy:
    EL-Sayed, Ahmed M.A.
    Ebead, Hanaa R.
    Powiązania:
    https://bibliotekanauki.pl/articles/1818643.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    self-reference
    quadratic integral equation
    existence of solutions
    uniqueness of solution
    continuous dependence
    Schauder fixed point theorem
    równanie całkowe
    rozwiązania
    zależność ciągła
    punkt stały Schaudera
    Opis:
    In this work we study the existence of positive monotonic solutions of a self-reference quadratic integral equation in the class of continuous real valued functions. The continuous dependence of the uniquesolution will be proved. Some examples will be given.
    Źródło:
    Journal of Mathematics and Applications; 2020, 43; 67--80
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fixed point theorems for monotone mappings in ordered Banach spaces under weak topology features
    Autorzy:
    Alahmari, Abdullah
    Mabrouk, Mohamed
    Taoudi, Mohamed-Aziz
    Powiązania:
    https://bibliotekanauki.pl/articles/357719.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    fixed point theorem
    order cone
    increasing operator
    decreasing operator
    weakly condensing
    measure of weak noncompactness
    twierdzenie o punkcie stałym
    stożek
    operator
    miara słabej niezgodności
    Opis:
    We present several fixed point theorems for monotone nonlinear operators in ordered Banach spaces. The main assumptions of our results are formulated in terms of the weak topology. As an application, we study the existence of solutions to a class of first-order vectorvalued ordinary differential equations. Our conclusions generalize many well-known results.
    Źródło:
    Journal of Mathematics and Applications; 2019, 42; 5-19
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New versions on Nikaidôs coincidence theorem
    Autorzy:
    Chu, Liang-Ju
    Lin, Ching-Yan
    Powiązania:
    https://bibliotekanauki.pl/articles/729530.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Vietoris map
    Nikaidô's coincidence theorem
    Fan-type element
    Górniewicz-type fixed point theorem
    coincidence
    variational inequality
    acyclic multifunction
    partition of unity
    local intersection property
    KKM mapping
    locally selectionable multifunction
    Opis:
    In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions, as well as some Górniewicz-type fixed point theorems. Beyond the realm of monotonicity nor metrizability, the results derived here generalize and unify various earlier ones from the classic optimization theory. In the sequel, we shall deduce two versions of Nikaidô's coincidence theorem about Vietoris maps from different approaches.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 1; 79-95
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Schauder’s fixed-point theorem in approximate controllability problems
    Autorzy:
    Babiarz, A.
    Klamka, J.
    Niezabitowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/329939.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    approximate controllability
    Banach space
    Hilbert space
    Schauder's fixed point theorem
    infinite dimensional space
    sterowalność aproksymacyjna
    przestrzeń Banacha
    przestrzeń Hilberta
    twierdzenie o punkcie stałym
    przestrzeń nieskończenie wymiarowa
    Opis:
    The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2016, 26, 2; 263-275
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with ψ-Caputo fractional derivative
    Autorzy:
    Wahash, Hanan A.
    Abdo, Mohammed S
    Panchal, Satish K.
    Powiązania:
    https://bibliotekanauki.pl/articles/122800.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional differential equations
    ψ-fractional integral and derivative
    existence and Ulam-Hyers stability
    fixed point theorem
    równania różniczkowe ułamkowe
    równania różniczkowe cząstkowe
    pochodna ułamkowa
    twierdzenie o punkcie stałym
    pochodna ułamkowa Caputo
    Opis:
    In this paper, we investigate the existence, uniqueness and Ulam-Hyers stability of solutions for nonlinear implicit fractional differential equations with boundary conditions involving a ψ-Caputo fractional derivative. The obtained results for the proposed problem are proved under a new approach and minimal assumptions on the function ƒ . The analysis is based upon the reduction of the problem considered to the equivalent integral equation, while some fixed point theorems of Banach and Schauder and generalized Gronwall inequality are employed to obtain our results for the problem at hand. Finally, the investigation is illustrated by providing a suitable example.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 89-101
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and Ulam-Hyers stability of the implicit fractional boundary value problem with ψ-Caputo fractional derivative
    Autorzy:
    Wahash, Hanan A.
    Abdo, Mohammed S
    Panchal, Satish K.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839794.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional differential equations
    ψ-fractional integral and derivative
    existence and Ulam-Hyers stability
    fixed point theorem
    równania różniczkowe ułamkowe
    równania różniczkowe cząstkowe
    pochodna ułamkowa
    twierdzenie o punkcie stałym
    pochodna ułamkowa Caputo
    Opis:
    In this paper, we investigate the existence, uniqueness and Ulam-Hyers stability of solutions for nonlinear implicit fractional differential equations with boundary conditions involving a ψ-Caputo fractional derivative. The obtained results for the proposed problem are proved under a new approach and minimal assumptions on the function ƒ. The analysis is based upon the reduction of the problem considered to the equivalent integral equation, while some fixed point theorems of Banach and Schauder and generalized Gronwall inequality are employed to obtain our results for the problem at hand. Finally, the investigation is illustrated by providing a suitable example.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 89-101
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Measures of noncompactness in a Banach algebra and their applications
    Autorzy:
    Dudek, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/357842.pdf
    Data publikacji:
    2017
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    Banach algebra
    integral equation of fractional order
    fixed point theorem
    asymptotic stability
    ultimate monotonicity
    measure of noncompactness
    algebra Banacha
    przestrzeń Banacha
    równanie całkowite rzędu ułamkowego
    twierdzenie o punkcie stałym
    stabilność asymptotyczna
    monotoniczność
    Opis:
    In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach.
    Źródło:
    Journal of Mathematics and Applications; 2017, 40; 69-84
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On positive solutions of a class of second order nonlinear differential equations on the halfline
    Autorzy:
    Staněk, Svatoslav
    Powiązania:
    https://bibliotekanauki.pl/articles/1311424.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    nonlinear second order differential equation
    nonnegative solution
    existence and uniqueness of solutions
    bounded solution
    dependence of solutions on the parameter
    boundary value problem on a noncompact interval
    Tikhonov-Schauder fixed point theorem
    Opis:
    The differential equation of the form $(q(t)k(u)(u')^a)' = f(t)h(u)u'$, a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u'(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
    Źródło:
    Annales Polonici Mathematici; 1995, 62, 2; 123-142
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Positive solution of a fractional differential equation with integral boundary conditions
    Autorzy:
    Abdo, M. S.
    Wahash, H. A.
    Panchal, S. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/122788.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional derivative and integral
    positive solutions of nonlinear boundary value problems
    upper and lower solutions
    fixed point theorem
    pochodna ułamkowa
    twierdzenie o punkcie stałym
    twierdzenia o punkcie stałym Schaudera
    równania różniczkowe cząstkowe
    nieliniowe cząstkowe równanie różniczkowe
    zagadnienie brzegowe
    Opis:
    In this paper, we prove the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional differential equations involving a Caputo fractional operator with integral boundary conditions. The technique used to prove our results depends on the upper and lower solution, the Schauder fixed point theorem and the Banach contraction principle. The result of existence obtained through constructing the upper and lower control functions of the nonlinear term without any monotone requirement.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 3; 5-15
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Key moments of the mutual influence of the Polish and Soviet schools of nonlinear functional analysis in the 1920s--1950s
    Autorzy:
    Bogatov, Egor Mikhailovich
    Powiązania:
    https://bibliotekanauki.pl/articles/749784.pdf
    Data publikacji:
    2017
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Polish school of functional analysis, Soviet school of functional analysis, fixed point theorem, Orlicz space, nonlinear integral equations, mapping degree, convex sets, retracts theory
    Polska szkoła analizy funkcjonalnej, radziecka szkoła analizy funkcjonalnej, twierdzenie o punkcie stałym, przestrzeń Orlicza, nieliniowe równanie całkowe, stopień odwzorowania, zbiory wypukłe, teoria retraktów
    Opis:
    Artykuł zawiera kluczowe aspekty historii rozwoju metod jakościowych nieliniowej analizy funkcjonalnej (twierdzenia o punkcie stałym, teoria stopnia odwzorowania, teoria przestrzeni Orlicza), w~ramach których najbardziej uwidoczniły się wzajemne oddziaływania polsko-radzieckie. Do połowy XX wieku w dziedzinach tych  dokonał się  postęp za sprawą  przedstawicieli lwowskiej szkoły matematycznej, warszawskiej szkoły matematycznej, moskiewskiej szkoły matematycznej  i odeskiej szkoły matematycznej. Analiza ich rezultatów stanowi główną część niniejszej pracy. Szczególną uwagę zwracamy na badania matematyka radzieckiego M. A. Krasnosel'skiego, który korzystał z wyników J. Schaudera i K. Borsuka oraz z przestrzeni Orlicza przy rozwiązywaniu szerokiej klasy problemów z jakościowej teorii nieliniowych równań całkowych.
    The paper includes key aspects of the history of development of qualitative methods of non-linear functional analysis (fixed point theorems, theory of mapping degree, theory of Orlicz spaces), within the framework of which Polish-Soviet interaction was most clearly manifested. In the period up to the mid-twentieth century these areas were advanced by the representatives of Lvov Mathematical School, Warsaw Mathematical School, Moscow Mathematical School and Odessa Mathematical School. Examination of their results is a significant part of this work. Much attention is paid to the investigations of the Soviet mathematician M.A. Krasnosel'skii, who used the achievements of J. Schauder and K. Borsuk as well as Orlicz spaces for solving a wide class of problems in qualitative theory of nonlinear integral equations. 
    Źródło:
    Antiquitates Mathematicae; 2017, 11
    1898-5203
    2353-8813
    Pojawia się w:
    Antiquitates Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stability by Krasnoselskiis theorem in totally nonlinear neutral differential equations
    Autorzy:
    Derrardjia, I.
    Ardjouni, A.
    Djoudi, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1397510.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fixed point
    stability
    nonlinear neutral equation
    Krasnoselskii-Burton theorem
    Opis:
    In this paper we use fixed point methods to prove asymptotic stability results of the zero solution of a class of totally nonlinear neutral differential equations with functional delay. The study concerns $x^\prime (t)= -a(t)x^3(t) + c(t)x^\prime (t-r(t)) + b(t) x^3 (t-r(t)) $. The equation has proved very challenging in the theory of Liapunov’s direct method. The stability results are obtained by means of Krasnoselskii-Burton’s theorem and they improve on the work of T.A. Burton (see Theorem 4 in [Liapunov functionals, fixed points, and stability by Krasnoselskii’s theorem, Nonlinear Studies 9 (2001), 181–190]) in which he takes c=0 in the above equation
    Źródło:
    Opuscula Mathematica; 2013, 33, 2; 255-272
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotic stability in the Schauder fixed point theorem
    Autorzy:
    Shih, Mau-Hsiang
    Wu, Jinn-Wen
    Powiązania:
    https://bibliotekanauki.pl/articles/1217906.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    fixed point
    asymptotic stability
    spectral radius
    compact map
    holomorphic map
    normal family
    Whitney smooth extension theorem
    Opis:
    This note presents a theorem which gives an answer to a conjecture which appears in the book Matrix Norms and Their Applications by Belitskiĭ and Lyubich and concerns the global asymptotic stability in the Schauder fixed point theorem. This is followed by a theorem which states a necessary and sufficient condition for the iterates of a holomorphic function with a fixed point to converge pointwise to this point.
    Źródło:
    Studia Mathematica; 1998, 131, 2; 143-148
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-69 z 69

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