Periodicity in multiple delay volterra difference equations of neutral type

Abstract

We prove the existence and uniqueness of a periodic solution for the multiple delay diference neutral Volterra equation ∆x(n) = −∑Nj=1aj (n)x(n − τj (n)) + ∆Q(n, x(n − τ1(n)), ..., x(n − τN (n))+∑Nj=1∑nn−τj (n) kj (n, s)fj (s, x(s)). The contraction mapping principle and a Krasnoselskii’s fxed point theorem are used in the analysis