Almost Automorphic Solutions of Difference Equations

We study discrete almost automorphic functions (sequences) defined on the set of integers with values in a Banach space [inline-graphic not available: see fulltext]. Given a bounded linear operator [inline-graphic not available: see fulltext] defined on [inline-graphic not available: see fulltext] and a discrete almost automorphic function [inline-graphic not available: see fulltext], we give criteria for the existence of discrete almost automorphic solutions of the linear difference equation [inline-graphic not available: see fulltext]. We also prove the existence of a discrete almost automorphic solution of the nonlinear difference equation [inline-graphic not available: see fulltext] assuming that [inline-graphic not available: see fulltext] is discrete almost automorphic in [inline-graphic not available: see fulltext] for each [inline-graphic not available: see fulltext], satisfies a global Lipschitz type condition, and takes values on [inline-graphic not available: see fulltext].