Almost Periodic Solutions of Nonlinear Discrete Volterra Equations with Unbounded Delay
نویسنده
چکیده
In this paper we study the existence of almost periodic solution for nonlinear discrete Volterra equation with unbounded delay, as a discrete version of the results for integro-differential equations. 1. Almost periodic sequences and difference equations Bohr’s theory of almost periodic functions has been extensively studied, especially in connection with differential equations. Almost periodic solutions of ordinary differential systems are vector valued functions defined on the set R of real numbers. But the notion of almost periodicity makes sense on any additive group other than R. Indeed, the Bohr definition for an almost periodic function is valid for vector doubly infinite sequences defined on the set Z of integers. This is important since infinite sequences are candidate solutions of difference equations. Also, the generalizations of almost periodic functions-asymptotic almost periodicity by Frechet, pseudo almost periodicity by Zhang can be defined on sequences. A sequence x : Z→ R is said to be almost periodic if for any ε > 0 there exists an integer l(ε) > 0 such that each interval of length l contains an integer τ for 2000 Mathematics Subject Classification. 39A11, 39A10.
منابع مشابه
Periodic solutions of discrete Volterra equations
In this paper, we investigate periodic solutions of linear and nonlinear discrete Volterra equations of convolution or non-convolution type with unbounded memory. For linear discrete Volterra equations of convolution type, we establish Fredholm’s alternative theorem and for equations of non-convolution type, and we prove that a unique periodic solution exists for a particular bounded initial fu...
متن کاملAlmost Periodic Solutions of Nonlinear Volterra Difference Equations with Unbounded Delay
In order to obtain the conditions for the existence of periodic and almost periodic solutions of Volterra difference equations, x(n+1) = f(n, x(n))+ ∑n s=−∞ F (n, s, x(n+ s), x(n)), we consider certain stability properties, which are referred to as (K, ρ)-weakly uniformly-asymptotic stability and (K, ρ)-uniformly asymptotic stability. Moreover, we discuss the relationship between the ρ-separati...
متن کاملConvergence of Numerical Method For the Solution of Nonlinear Delay Volterra Integral Equations
In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...
متن کاملEXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY
متن کامل
Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations
In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...
متن کامل