The large contraction principle and existence of periodic solutions for infinite delay Volterra difference equations

Abstract

In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinitedelay Volterra difference equation: mathrm{Δx}(n)=p(n)+b(n)h(x(n))+sum_{mathrm k=-infty}^{mathrm n}B(n,k)g(x(k)).We employ a Krasnosel’skiĭ type fixed point theorem, originally proved by Burton. The primary sufficient condition isnot verifiable in terms of the parameters of the difference equation, and so we provide three applications in which theprimary sufficient condition is verified.