EXISTENCE CRITERIA FOR NONLINEAR URYSOHN DIFFERENCE EQUATIONS IN BANACH SPACES

Abstract

We use Monch's nonlinear alternative of Leray-Schauder type to establish general existence principles for the Urysohn discrete equation y(i) =sum_{j=0}^N f(i,j,y(j)) for i in {0,1,...,T}. Here y takes values in a Banach space and the kernel f satisfies a local set-Lipschitz condition.