Existence of Bounded Solutions of Nonlinear Difference Equations in Banach Spaces

Abstract

We establish sufficient conditions for the existence of bounded solutions of the nonlinear difference equations $$ x\left( {n+1} \right)=F\left( {n,x(n)} \right)x(n)+f(n),\;n\in \mathbb{Z} $$ , in a Banach space.