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    Wyświetlanie 1-11 z 11
    Tytuł:
    A version of non-Hamiltonian Liouville equation
    Autorzy:
    Rom, Celina
    Powiązania:
    https://bibliotekanauki.pl/articles/729554.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Liouville equation
    invariant measure
    Opis:
    In this paper we give a version of the theorem on local integral invariants of systems of ordinary differential equations. We give, as an immediate conclusion of this theorem, a condition which guarantees existence of an invariant measure of local dynamical systems. Results of this type lead to the Liouville equation and have been frequently proved under various assumptions. Our method of the proof is simpler and more direct.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 1; 5-14
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the semilinear integro-differential nonlocal Cauchy problem
    Autorzy:
    Majcher, Piotr
    Roszak, Magdalena
    Powiązania:
    https://bibliotekanauki.pl/articles/729610.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    integro-differential equations
    measure of weak non-compactness
    non-local problem
    Opis:
    In this paper, we prove an existence theorem for the pseudo-non-local Cauchy problem $x'(t) + Ax(t) = f(t,x(t),∫_{t₀}^{t} k(t,s,x(s))ds)$, x₀(t₀) = x₀ - g(x), where A is the infinitesimal generator of a C₀ semigroup of operator ${T(t)}_{t > 0}$ on a Banach space. The functions f,g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2005, 25, 1; 5-18
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    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:
    Asymptotic behaviour of solutions of difference equations in Banach spaces
    Autorzy:
    Kisiołek, Anna
    Powiązania:
    https://bibliotekanauki.pl/articles/729477.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Banach space
    difference equation
    fixed point
    measure of noncompactness
    asymptotic behaviour of solutions
    Opis:
    In this paper we consider the first order difference equation in a Banach space
    $Δx_{n} = ∑_{i=0}^∞ a^{i}_{n} f(x_{n+i})$.
    We show that this equation has a solution asymptotically equal to a.
    As an application of our result we study the difference equation
    $Δx_{n} = ∑_{i=0}^∞ a^i_{n}g(x_{n+i}) + ∑_{i=0}^∞ b^{i}_{n}h(x_{n+i}) + y_{n}$
    and give conditions when this equation has solutions.
    In this note we extend the results from [8,9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 5-13
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Abstract inclusions in Banach spaces with boundary conditions of periodic type
    Autorzy:
    Guedda, Lahcene
    Hallouz, Ahmed
    Powiązania:
    https://bibliotekanauki.pl/articles/729484.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    measure of noncompactness
    condensing operator
    nonlinear abstract inclusion
    accretive operator
    integral solution
    nonlinear semigroup
    Opis:
    We study in the space of continuous functions defined on [0,T] with values in a real Banach space E the periodic boundary value problem for abstract inclusions of the form
    ⎧ $x ∈ S(x(0), sel_{F}(x))$
    ⎨
    ⎩ x (T) = x(0),
    where, $F:[0,T] × → 2^E \∅$ is a multivalued map with convex compact values, ⊂ E, $sel_{F}$ is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed by m-accretive operators generating not necessarily a compact semigroups.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 2; 229-253
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    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:
    Differential inclusions and multivalued integrals
    Autorzy:
    Cichoń, Kinga
    Cichoń, Mieczysław
    Satco, Bianca
    Powiązania:
    https://bibliotekanauki.pl/articles/729320.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    nonlocal Cauchy problem
    Aumann integrals
    Pettis integrals
    Henstock-Kurzweil-Pettis integrals
    measure of weak noncompactness
    Opis:
    In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces
    x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I.
    Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented by a short survey about multivalued integration including Pettis and Henstock-Kurzweil-Pettis multivalued integrals.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 171-191
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals
    Autorzy:
    Kubiaczyk, Ireneusz
    Sikorska-Nowak, Aneta
    Powiązania:
    https://bibliotekanauki.pl/articles/729401.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Cauchy dynamic problem
    Banach space
    measure of noncompactness
    Carathéodory's type solutions
    time scales
    fixed point
    Opis:
    In the paper, we prove the existence of solutions and Carathéodory's type solutions of the dynamic Cauchy problem
    $x^Δ(t) = f(t,x(t))$, t ∈ T,
    x(0) = x₀,
    where T denotes an unbounded time scale (a nonempty closed subset of R and such that there exists a sequence (xₙ) in T and xₙ → ∞) and f is continuous or satisfies Carathéodory's conditions and some conditions expressed in terms of measures of noncompactness. The Sadovskii fixed point theorem and Ambrosetti's lemma are used to prove the main result. The results presented in the paper are new not only for Banach valued functions, but also for real-valued functions.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 113-126
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control
    Autorzy:
    Ahmed, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/729584.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    stochastic differential equations
    Hilbert space
    measurable vector fields
    finitely additive measure solutions
    optimal feedback controls
    Opis:
    In this paper, we consider a class of semilinear stochastic evolution equations on Hilbert space driven by a stochastic vector measure. The nonlinear terms are assumed to be merely continuous and bounded on bounded sets. We prove the existence of measure valued solutions generalizing some earlier results of the author. As a corollary, an existence result of a measure solution for a forward Kolmogorov equation with unbounded operator valued coefficients is obtained. The main result is further extended to cover Borel measurable drift and diffusion which are assumed to be bounded on bounded sets. Also we consider control problems for these systems and present several results on the existence of optimal feedback controls.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2005, 25, 1; 129-157
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An abstract Cauchy problem for higher order functional differential inclusions with infinite delay
    Autorzy:
    Ke, Tran
    Obukhovskii, Valeri
    Wong, Ngai-Ching
    Yao, Jen-Chih
    Powiązania:
    https://bibliotekanauki.pl/articles/729357.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Cauchy problem
    functional differential inclusion
    infinite delay
    higher order
    existence family
    phase space
    fixed point
    multivalued map
    measure of noncompactness
    condensing map
    Opis:
    The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 2; 199-229
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Integro-differential equations on time scales with Henstock-Kurzweil delta integrals
    Autorzy:
    Sikorska-Nowak, Aneta
    Powiązania:
    https://bibliotekanauki.pl/articles/729234.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    integro-differential equations
    nonlinear Volterra integral equation
    time scales
    Henstock-Kurzweil delta integral
    HL delta integral
    Banach space
    fixed point
    measure of noncompactness
    Carathéodory solutions
    Opis:
    In this paper we prove existence theorems for integro - differential equations
    $x^Δ (t) = f(t,x(t),∫₀^t k(t,s,x(s))Δs)$,
    t ∈ Iₐ = [0,a] ∩ T, a ∈ R₊,
    x(0) = x₀
    where T denotes a time scale (nonempty closed subset of real numbers R), Iₐ is a time scale interval. Functions f,k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral.
    Additionally, functions f and k satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. Moreover, we prove an Ambrosetti type lemma on a time scale.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 1; 71-90
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-11 z 11

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