Almost Periodic Solutions of Nonlinear Volterra Difference Equations with Unbounded Delay

• Main Authors: Yoshihiro Hamaya, Tomomi Itokazu, Kaori Saito
• Format: Article
• Language: English
• Published: MDPI AG 2015-08-01
• Series: Axioms
• Subjects: almost periodic solutions; Volterra difference equations; (K, p)-relatively weakly uniformly-asymptotically stable; p-separation conditions
• Online Access: http://www.mdpi.com/2075-1680/4/3/345
• ISSN: 2075-1680

In order to obtain the conditions for the existence of periodic and almost periodic solutions of Volterra difference equations, \( x(n+1)=f(n,x(n))+\sum_{s=-\infty}^{n}F(n,s, {x(n+s)},x(n)) \), we consider certain stability properties, which are referred to as (K, \( \rho \))-weakly uniformly-asymptotic stability and (K, \( \rho \))-uniformly asymptotic stability. Moreover, we discuss the relationship between the \( \rho \)-separation condition and the uniformly-asymptotic stability property in the \( \rho \) sense.