Browsing by Subject "difference equations"
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Item type:Article, Access status: Open Access , A note on nonlocal discrete problems involving sign-changing Kirchhoff functions(Wydawnictwa AGH, 2025) Ricceri, BiagioIn this note, we establish a multiplicity theorem for a nonlocal discrete problem of the type \[\begin{cases} -\left(a\sum_{m=1}^{n+1}|x_m-x_{m-1}|^2+b\right)(x_{k+1}-2x_k+x_{k-1})=h_k(x_k), &k=1,\ldots ,n, \\ x_0=x_{n+1}=0 \end{cases}\] assuming \(a\gt 0\) and (for the first time) \(b\gt 0\).Item type:Article, Access status: Open Access , Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian(2014) Candito, Pasquale; D’Aguí, GiuseppinaIn this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete $p$-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.Item type:Article, Access status: Open Access , Difference equations with impulses(Wydawnictwa AGH, 2019) Danca, Marius; Fečkan, Michal; Pospíšil, MichalDifference 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.Item type:Thesis, Access status: Restricted , Metoda iteracyjno-projekcyjna dla pewnej klasy równań różnicowych(Data obrony: 2013-07-23) Gorzkowska, Aleksandra
Wydział Matematyki StosowanejItem type:Article, Access status: Open Access , New aspects for the oscillation of first-order difference equations with deviating arguments(Wydawnictwa AGH, 2022) Attia, Emad R.; El-Matary, Bassant M.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.Item type:Article, Access status: Open Access , New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments(Wydawnictwa AGH, 2022) Attia, Emad R.; El-Matary, Bassant M.; Chatzarakis, George E.In this paper, we study the oscillatory behavior of the solutions of a first-order difference equation with non-monotone retarded argument and nonnegative coefficients, based on an iterative procedure. We establish some oscillation criteria, involving $\lim \sup$, which achieve a marked improvement on several known conditions in the literature. Two examples, numerically solved in MAPLE software, are also given to illustrate the applicability and strength of the obtained conditions.Item type:Article, Access status: Open Access , On oscillatory solutions of certain difference equations(2006) Grzegorczyk, Grzegorz; Werbowski, JarosławSome 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 foroscillation of solutions of the equations discussed.Item type:Article, Access status: Open Access , On the global attractivity and the periodic character of a recursive sequence(2010) Elsayed, E. M.In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence $x_{n+1} = ax_n + \frac{bx_{n-1}+cx_{n+2}}{dx_{n-1}+ex_{n+2}}, \quad n=0,1,\ldots,$, where the parameters $a$, $b$, $c$, $d$ and $e$ are positive real numbers and the initial conditions $x_{-2}$, $x_{-1}$ and $x_{0}$ are positive real numbers.Item type:Article, Access status: Open Access , On the stability of some systems of exponential difference equations(Wydawnictwa AGH, 2018) Psarros, Nikolaos; Papaschinopoulos, Garyfalos; Schinas, Christos J.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.Item type:Article, Access status: Open Access , Oscillation conditions for difference equations with several variable delays(Wydawnictwa AGH, 2023) El-Matary, Bassant M.; El-Morshedy, Hassan A.; Benekas, Vasileios; Stavroulakis, Ioannis P.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.Item type:Article, Access status: Open Access , Oscillation criteria for linear difference equations with several variable delays(Wydawnictwa AGH, 2021) Benekas, Vasileios; Garab, Ábel; Kashkynbayev, Ardak; Stavroulakis, Ioannis P.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.Item type:Article, Access status: Open Access , Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences(2006) Schmeidel, EwaIn 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.Item type:Thesis, Access status: Restricted , Równania różnicowe(Data obrony: 2010-07-08) Pająk, Marcin
Wydział Matematyki StosowanejItem type:Thesis, Access status: Restricted , Zastosowanie teorii równań różnicowych do ciągłego i dyskretnego modelu Malthusa(Data obrony: 2016-04-28) Aksamit, Natalia
Wydział Matematyki Stosowanej