On the Existence of Almost Automorphic Solutions of Volterra Difference Equations

Given a complex summable sequence and a discrete almost automorphic function with values in a complex Banach space X, we give criteria for the existence of discrete almost automorphic solutions of the linear Volterra difference equation, for ? in a distinguished subset of the complex plane, determined by a(n). We also prove the existence of a discrete almost automorphic solution of the nonlinear Volterra difference equation u(n + 1) =, where f(n, x)is a discrete almost automorphic function in n for each x ? X that satisfies a global Lipschitz condition and takes values in X. Finally, we treat the same type of problem for Volterra functional difference equations. © 2012 Copyright Taylor and Francis Group, LLC.