Periodic and asymptotically periodic solutions of systems of nonlinear difference equations with infinite delay

Abstract

In this work we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the existence of such periodic solutions.

Existence of The Asymptotically Periodic Solution to the System of Nonlinear Neutral Difference Equations

“…Since any periodic sequence is bounded, then the conditions ensuring existence of a periodic solution of (1) are sufficient for existence of bounded solution to system (1). Therefore, results presented here are complementary to the results obtained in [17].…”

“…Here, conditions for the existence of asymptotically periodic solution are presented. Asymptotically periodic solutions were investigated among others for Volterra difference equations in [1,[6][7][8][9][10] as well as in [4,14] for the rational difference equations.…”

On the existence and uniqueness of ( N , λ ) $(N,\lambda )$ -periodic solutions to a class of Volterra difference equations

“…On the other hand, problems of existence and uniqueness of periodic and anti-periodic solutions of Volterra difference equations have been considered by several authors due to their various applications in mathematical biology, problems related to signals and systems, integral equations, the foundation of functional analysis and numerical methods for solving Volterra integral or integro-differential equations. The papers [1,4,8,10,14] cover many of these applications. Araya et al in [6] studied the existence and uniqueness of almost automorphic discrete solutions for a class of nonlinear Volterra difference equations of convolution type on a Banach space X with norm • X , namely…”

“…Author details 1 Departamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla, Colombia. 2 Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Santiago, Chile.…”

Almost periodic solutions of Volterra difference systems

“…Qualitative properties of Volterra equations on continuous, discrete and hybrid domains became topic of many studies in the literature. By a quick literature review, we refer to [1][2][3][4][5][6][7][8][9] and references therein. Investigation of periodic solutions of dynamic equations and systems with periodic structures is of special importance for studies on population dynamics and control theory.…”