Advances in Difference Equations
Volume 2009 (2009), Article ID 591380, 15 pages
Research Article

Almost Automorphic Solutions of Difference Equations

Departamento de Matemática, Universidad de Santiago, 9160000 Santiago, Chile

Received 25 March 2009; Accepted 13 May 2009

Academic Editor: Mouffak Benchohra

Copyright © 2009 Daniela Araya et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study discrete almost automorphic functions (sequences) defined on the set of integers with values in a Banach space X. Given a bounded linear operator T defined on X and a discrete almost automorphic function f(n), we give criteria for the existence of discrete almost automorphic solutions of the linear difference equation Δu(n)=Tu(n)+f(n). We also prove the existence of a discrete almost automorphic solution of the nonlinear difference equation Δu(n)=Tu(n)+g(n,u(n)) assuming that g(n,x) is discrete almost automorphic in n for each xX, satisfies a global Lipschitz type condition, and takes values on X.