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Tytuł:
Difference equations with impulses
Autorzy:
Danca, Marius
Feckan, Michal
Pospisil, Michal
Powiązania:
https://bibliotekanauki.pl/articles/255372.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
difference equations
impulses
stability
fixed points
Li-Yorke chaos
Opis:
Difference equations with impulses are studied focussing on the existence of periodic or bounded orbits, asymptotic behavior and chaos. So impulses are used to control the dynamics of the autonomous difference equations. A model of supply and demand is also considered when Li-Yorke chaos is shown among others.
Źródło:
Opuscula Mathematica; 2019, 39, 1; 5-22
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On oscillatory solutions of certain difference equations
Autorzy:
Grzegorczyk, G.
Werbowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/255794.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
difference equations
oscillation
Opis:
Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 317-326
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Polynomial quasisolutions of linear differential-difference equations
Autorzy:
Cherepennikov, V. B.
Ermolaeva, P. G.
Powiązania:
https://bibliotekanauki.pl/articles/255903.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
differential-difference equations
neutral type
initial-value problem
polynomial quasisolution
Opis:
The paper discusses a linear differential-difference equation of neutral type with linear coefficients, when at the initial time moment t = 0 the value of the desired function x(t) is known. The authors are not familiar with any results which would state the solvability conditions for the given problem in the class of analytical functions. A polynomial of some degree N is introduced into the investigation. Then the term "polynomial quasisolution" (PQ-solution) is understood in the sense of appearance of the residual Δ(t) = O(tN), when this polynomial is substituted into the initial problem. The paper is devoted to finding PQ-solutions for the initial-value problem under analysis.
Źródło:
Opuscula Mathematica; 2006, 26, 3; 431-443
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some stability conditions for scalar Volterra difference equations
Autorzy:
Berezansky, L.
Migda, M.
Schmeidel, E.
Powiązania:
https://bibliotekanauki.pl/articles/254995.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
linear and nonlinear Volterra difference equations
boundedness of solutions
exponential and asymptotic stability
Opis:
New explicit stability results are obtained for the following scalar linear difference equation [formula] and for some nonlinear Volterra difference equations.
Źródło:
Opuscula Mathematica; 2016, 36, 4; 459-470
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exponential stability results for variable delay difference equations
Autorzy:
Yankson, Ernest
Powiązania:
https://bibliotekanauki.pl/articles/1397336.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
exponential stability
Lyapunov functional
instability.
Opis:
Sufficient conditions that guarantee exponential decay to zero of the variable delay difference equation $x(n + 1) = a(n)x(n) + b(n)x(n − g(n))$ are obtained. These sufficient conditions are deduced via inequalities by employing Lyapunov functionals. In addition, a criterion for the instability of the zero solution is established. The results in the paper generalizes some results in the literature.
Źródło:
Opuscula Mathematica; 2021, 41, 1; 145-155
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Variation of constant formulas for fractional difference equations
Autorzy:
Anh, P. T.
Babiarz, A.
Czornik, A.
Niezabitowski, M.
Siegmund, S.
Powiązania:
https://bibliotekanauki.pl/articles/229367.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
fractional difference equation
variation of constant
separation of solutions
Opis:
In this paper, we establish variation of constant formulas for both Caputo and Riemann-Liouville fractional difference equations. The main technique is the Z-transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.
Źródło:
Archives of Control Sciences; 2018, 28, 4; 617-633
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillation criteria for even order neutral difference equations
Autorzy:
Selvarangam, S.
Rupadevi, S. A.
Thandapani, E.
Pinelas, S.
Powiązania:
https://bibliotekanauki.pl/articles/255009.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
even order
neutral difference equation oscillation
asymptotic behavior
mixed type
Opis:
In this paper, we present some new sufficient conditions for oscillation of even order nonlinear neutral difference equation of the form [formula] where m ≥ 2 is an even integer, using arithmetic-geometric mean inequality. Examples are provided to illustrate the main results.
Źródło:
Opuscula Mathematica; 2019, 39, 1; 91-108
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:
Existence of three solutions for perturbed nonlinear difference equations
Autorzy:
Heidarkhani, S.
Moghadam, M. K.
Powiązania:
https://bibliotekanauki.pl/articles/952774.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
nonlinear difference equations
discrete boundary value problem
three solutions
critical point theory
variational methods
Opis:
Using critical point theory, we study the existence of at least three solutions for perturbed nonlinear difference equations with discrete boundary-value condition depending on two positive parameters.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 747-761
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Operators commuting with translations, and systems of difference equations
Autorzy:
Laczkovich, Miklós
Powiązania:
https://bibliotekanauki.pl/articles/965844.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
Let ${\mathcal B} ={f:ℝ → ℝ: f is bounded}$, and ${\mathcal M} ={f:ℝ → ℝ: f is Lebesgue measurable}$. We show that there is a linear operator $Φ :{\mathcal B} → {\mathcal M}$ such that Φ(f)=f a.e. for every $f ∈ {\mathcal B} ∩ {\mathcal M}$, and Φ commutes with all translations. On the other hand, if $Φ : {\mathcal B} → {\mathcal M}$ is a linear operator such that Φ(f)=f for every $f ∈ {\mathcal B} ∩ {\mathcal M}$, then the group $G_Φ$ ={ a ∈ ℝ:Φ commutes with the translation by a} is of measure zero and, assuming Martin's axiom, is of cardinality less than continuum. Let Φ be a linear operator from $ℂ^ℝ$ into the space of complex-valued measurable functions. We show that if Φ(f) is non-zero for every $f(x)=e^{cx}$, then $G_Φ$ must be discrete. If Φ(f) is non-zero for a single polynomial-exponential f, then $G_Φ$ is countable, moreover, the elements of $G_Φ$ are commensurable. We construct a projection from $ℂ^ℝ$ onto the polynomials that commutes with rational translations. All these results are closely connected with the solvability of certain systems of difference equations.
Źródło:
Colloquium Mathematicum; 1999, 80, 1; 1-22
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions of fractional nabla difference equations - existence and uniqueness
Autorzy:
Jonnalagadda, J. M.
Powiązania:
https://bibliotekanauki.pl/articles/255136.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
nabla difference
exponential function
fixed point
existence
uniqueness
continuous dependence
Opis:
In this article, we discuss existence, uniqueness and dependency of solutions of nonlinear fractional nabla difference equations in a Banach space equipped with a suitable norm, using the contractive mapping approach. As an application of the established results we present and analyse a few examples.
Źródło:
Opuscula Mathematica; 2016, 36, 2; 215-238
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillation conditions for difference equations with several variable delays
Autorzy:
El-Matary, Bassant M.
El-Morshedy, Hassan A.
Benekas, Vasileios
Stavroulakis, Ioannis P.
Powiązania:
https://bibliotekanauki.pl/articles/29519474.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
oscillation
difference equations
non-monotone delays
first order
Opis:
A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result.
Źródło:
Opuscula Mathematica; 2023, 43, 6; 789-801
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillation criteria for linear difference equations with several variable delays
Autorzy:
Benekas, Vasileios
Garab, Ábel
Kashkynbayev, Ardak
Stavroulakis, Ioannis P.
Powiązania:
https://bibliotekanauki.pl/articles/2049029.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
oscillation
difference equations
several delays
non-monotone argument
slowly varying function
Opis:
We obtain new sufficient criteria for the oscillation of all solutions of linear delay difference equations with several (variable) finite delays. Our results relax numerous well-known limes inferior-type oscillation criteria from the literature by letting the limes inferior be replaced by the limes superior under some additional assumptions related to slow variation. On the other hand, our findings generalize an oscillation criterion recently given for the case of a constant, single delay.
Źródło:
Opuscula Mathematica; 2021, 41, 5; 613-627
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the stability of some systems of exponential difference equations
Autorzy:
Psarros, N.
Papaschinopoulos, G.
Schinas, C.J.
Powiązania:
https://bibliotekanauki.pl/articles/255823.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
difference equations
asymptotic behaviour
global stability
centre manifold
biological dynamics
Opis:
In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
Źródło:
Opuscula Mathematica; 2018, 38, 1; 95-115
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Representations of quantum groups and (conditionally) invariant q-difference equations
Autorzy:
Dobrev, Vladimir
Powiązania:
https://bibliotekanauki.pl/articles/1342758.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
We give a systematic discussion of the relation between q-difference equations which are conditionally $U_q()$-invariant and subsingular vectors of Verma modules over $U_q()$ (the Drinfeld-Jimbo q-deformation of a semisimple Lie algebra over ℂg or ℝ). We treat in detail the cases of the conformal algebra, = su(2,2), and its complexification, = sl(4). The conditionally invariant equations are the q-deformed d'Alembert equation and a new equation arising from a subsingular vector proposed by Bernstein-Gel'fand-Gel'fand.
Źródło:
Banach Center Publications; 1997, 40, 1; 203-222
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillatory properties of fourth order nonlinear difference equations with quasidifferences
Autorzy:
Schmeidel, E.
Migda, M.
Musielak, A.
Powiązania:
https://bibliotekanauki.pl/articles/255808.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
nonlinear difference equation
oscillatory solution
nonoscillatory solution
fourth order
Opis:
In this paper we present the oscillation criterion for a class of fourth order nonlinear difference equations with quasidifferences.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 371-380
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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:
Construction of an integral manifold for linear differential-difference equations
Autorzy:
Janglajew, K. R.
Valeev, K. G.
Powiązania:
https://bibliotekanauki.pl/articles/255899.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
system with deviating argument
integral manifold of solutions
fundamental matrix
exponential dichotomy
Opis:
In this paper we establish sufficient conditions for the existence of an asymptotic integral manifold of solutions of a linear system of differential-difference equations with a small parameter. This integral manifold is described by a linear system of differential equations without deviating argument.
Źródło:
Opuscula Mathematica; 2006, 26, 3; 465-470
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Reconstruction of potential and boundary conditions for second order difference equations
Autorzy:
Currie, Sonja
Love, Anne
Powiązania:
https://bibliotekanauki.pl/articles/962820.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Difference equations
inverse problem
boundary value problems
potential
eigenvalues
Opis:
Assume the eigenvalues and the weights are given for a difference boundary value problem and that the form of the boundary conditions at the endpoints is known. In particular, it is known whether the endpoints are fixed (i.e. Dirichlet or non-Dirichlet boundary conditions) or whether the endpoints are free to move (i.e. boundary conditions with affine dependence on the eigenparameter). This work illustrates how the potential as well as the exact boundary conditions can be uniquely reconstructed. The procedure is inductive on the number of unit intervals. This paper follows along the lines of S. Currie and A. Love, Inverse problems for difference equations with quadratic eigenparameter dependent boundary conditions, \emph{Quaestiones Mathematicae}, 40 (2017), no. 7, 861−877. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in the above reference, an additional spectrum is required more often than was the case in the unique reconstruction of the potential alone.
Źródło:
Commentationes Mathematicae; 2018, 58, 1-2; 1-9
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations
Autorzy:
Migda, M.
Powiązania:
https://bibliotekanauki.pl/articles/255688.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
neutral difference equation
asymptotic behavior
nonoscillatory solution
Opis:
In this paper we study asymptotic behavior of solutions of a higher order neutral difference equation of the form Δm(xn + pnxn-τ) + f(n, xσ(n)) = hn. We present conditions under which all nonoscillatory solutions of the above equation have the property xn = cnm-1 + o(nm-1) for some c ∈ R.
Źródło:
Opuscula Mathematica; 2006, 26, 3; 507-514
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
General solutions of second-order linear difference equations of Euler type
Autorzy:
Hongyo, A.
Yamaoka, N.
Powiązania:
https://bibliotekanauki.pl/articles/256019.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Euler-Cauchy equations
oscillation
conditionally oscillatory
Opis:
The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation [formula] or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.
Źródło:
Opuscula Mathematica; 2017, 37, 3; 389-402
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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:
Oscillation of third-order delay difference equations with negative damping term
Autorzy:
Bohner, Martin
Geetha, Srinivasan
Selvarangam, Srinivasan
Thandapani, Ethiraju
Powiązania:
https://bibliotekanauki.pl/articles/746986.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Third-order delay difference equation
comparison theorems
oscillation
asymptotic behavior
Opis:
The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from its relation to certain associated first-order delay difference equations or inequalities. Examples are given to illustrate the main results.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2018, 72, 1
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Construction of algebraic and difference equations with a prescribed solution space
Autorzy:
Moysis, L.
Karampetakis, N. P.
Powiązania:
https://bibliotekanauki.pl/articles/330046.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
algebraic equation
difference equation
behavior
exact modeling
autoregressive representation
discrete time system
higher order system
równanie algebraiczne
równanie różnicowe
system czasu dyskretnego
system wyższego rzędu
Opis:
This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ) β (k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ) . This work deals with the inverse problem of constructing a family of polynomial matrices A(σ) such that the system A(σ) β (k) = 0 satisfies some given forward and backward behavior. Initially, the connection between the backward behavior of an AR representation and the forward behavior of its dual system is showcased. This result is used to construct a system satisfying a certain backward behavior. By combining this result with the method provided by Gohberg et al. (2009) for constructing a system with a forward behavior, an algorithm is proposed for computing a system satisfying the prescribed forward and backward behavior.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 1; 19-32
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences
Autorzy:
Schmeidel, E.
Powiązania:
https://bibliotekanauki.pl/articles/255806.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
linear
nonlinear
difference equations
third order
oscillatory solution
quasidifferences
Riccati technique
Opis:
In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 361-369
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kneser-type oscillation criteria for second-order half-linear advanced difference equations
Autorzy:
Indrajith, N.
Graef, John R.
Thandapani, E.
Powiązania:
https://bibliotekanauki.pl/articles/2048703.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
second-order difference equations
advanced argument
half-linear
oscillation
Opis:
The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.
Źródło:
Opuscula Mathematica; 2022, 42, 1; 55-64
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillation of solutions to non-linear difference equations with several advanced arguments
Autorzy:
Pinelas, S.
Dix, J. G.
Powiązania:
https://bibliotekanauki.pl/articles/255605.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
advanced difference equation
non-oscillatory solution
Opis:
This work concerns the oscillation and asymptotic properties of solutions to the non-linear difference equation with advanced arguments [formula]. We establish sufficient conditions for the existence of positive, and negative solutions. Then we obtain conditions for solutions to be bounded, convergent to positive infinity and to negative infinity and to zero. Also we obtain conditions for all solutions to be oscillatory.
Źródło:
Opuscula Mathematica; 2017, 37, 6; 887-898
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillatory properties of solutions of the fourth order difference equations with quasidifferences
Autorzy:
Jankowski, R.
Schmeidel, E.
Zonenberg, J.
Powiązania:
https://bibliotekanauki.pl/articles/255677.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fourth-order difference equation
neutral type
quickly oscillatory solutions
almost oscillatory
Opis:
A class of fourth-order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four-dimensional difference system. The sufficient conditions under which the considered equation has no quickly oscillatory solutions are given. Finally, the sufficient conditions under which the equation is almost oscillatory are presented.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 789-797
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Reduction and continuation theorems for Brouwer degree and applications to nonlinear difference equations
Autorzy:
Mawhin, J.
Powiązania:
https://bibliotekanauki.pl/articles/255344.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Brouwer degree
nonlinear difference equations
Opis:
The aim of this note is to describe the continuation theorem of [39,40] directly in the context of Brouwer degree, providing in this way a simple frame for multiple applications to nonlinear difference equations, and to show how the corresponding reduction property can be seen as an extension of the well-known reduction formula of Leray and Schauder [24], which is fundamental for their construction of Leray-Schauder's degree in normed vector spaces.
Źródło:
Opuscula Mathematica; 2008, 28, 4; 541-560
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions of a class of singular linear systems of difference equations. Part 1
Autorzy:
Kanan, Asmaa M.
Powiązania:
https://bibliotekanauki.pl/articles/1030103.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Drazin inverse
Rank
Singular difference equations
Opis:
We extend results of Campbell, Meyer, Jr. and Rose of applications of the Drazine inverse to linear systems of differential equations with singular constant coefficients to solutions of linear systems of difference equations A x_(n+1)+B x_n= f_n ,n≥0 when A and B are m×m complex matrices and may both singular, under conditions that rank(A)=1 and trace of A is not equal zero. f_n is an arbitrary function in C^m, and x_n∈C^m. We give a new closed form for all solutions of those systems when they are tractable, using the theory of the Drazin inverse, and a matrix K∈C^(m×m).
Źródło:
World Scientific News; 2020, 143; 53-66
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New aspects for the oscillation of first-order difference equations with deviating arguments
Autorzy:
Attia, Emad R.
El-Matary, Bassant M.
Powiązania:
https://bibliotekanauki.pl/articles/2216188.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
difference equations
oscillation
non-monotone advanced arguments
Opis:
We study the oscillation of first-order linear difference equations with non-monotone deviating arguments. Iterative oscillation criteria are obtained which essentially improve, extend, and simplify some known conditions. These results will be applied to some numerical examples.
Źródło:
Opuscula Mathematica; 2022, 42, 3; 393-413
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weak heteroclinic solutions and competition phenomena to anisotropic difference equations with variable exponents
Autorzy:
Guiro, A.
Kone, B.
Ouaro, S.
Powiązania:
https://bibliotekanauki.pl/articles/952771.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
anisotropic difference equations
heteroclinic solutions
discrete Hölder type inequality
competition phenomena
Opis:
In this paper, we prove the existence of weak heteroclinic solutions for a family of anisotropic difference equations under competition phenomena between parameters.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 733-745
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions of a class of singular linear systems of difference equations. Part 2
Autorzy:
Kanan, Asmaa M.
Powiązania:
https://bibliotekanauki.pl/articles/1030133.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Drazin inverse
Moore-Penrose generalized inverse
Singular linear difference systems
Opis:
We extend results of Campbell of the linear systems of differential equations A x ̇+ Bx=f when A and B are rectangular, and results of Kanan of solution of a class of singular linear systems of difference equations A x_(n+1)+ Bx_n=f_n when A and B are square, to such systems of difference equations when A and B are rectangular. Explicit solutions of the last one are derived for several cases. One such is, when the matrix (λA+B) is one-to-one, another case is when such matrix is onto, for a scalar λ∈C. Also, explicit solutions are derived for the case that A is onto, and for the case that B is onto.
Źródło:
World Scientific News; 2020, 143; 127-138
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the nonoscillatory behavior of solutions of three classes of fractional difference equations
Autorzy:
Grace, Said Rezk
Alzabut, Jehad
Punitha, Sakthivel
Muthulakshmi, Velu
Adiguzel, Hakan
Powiązania:
https://bibliotekanauki.pl/articles/255333.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Caputo difference operator
nonoscillation criteria
fractional difference equation mathematical inequalities
Opis:
In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transfor mation technique, we employ herein an easily verifiable approach based on the fractional Taylor’s difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark.
Źródło:
Opuscula Mathematica; 2020, 40, 5; 549-568
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Eigenvalue-eigenfunction problem for Steklovs smoothing operator and differential-difference equations of mixed type
Autorzy:
Iakovlev, S. I.
Iakovleva, V.
Powiązania:
https://bibliotekanauki.pl/articles/254795.pdf
Data publikacji:
2013
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Steklov's smoothing operator
spectrum
eigenvalues
eigenfunctions
mixed-type differential-difference equations
initial function
method of steps
countably normed space
transformation group
generator
Opis:
It is shown that any μ ∈ C is an infinite multiplicity eigenvalue of the Steklov smoothing operator Sh acting on the space [formula]. For μ ≠ 0 the eigenvalue-eigenfunction problem leads to studying a differential-difference equation of mixed type. An existence and uniqueness theorem is proved for this equation. Further a transformation group is defined on a countably normed space of initial functions and the spectrum of the generator of this group is studied. Some possible generalizations are pointed out.
Źródło:
Opuscula Mathematica; 2013, 33, 1; 81-98
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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