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 . Given a bounded linear operator defined on and a discrete almost automorphic function , we give criteria for the existence of discrete almost automorphic solutions of the linear difference
equation . We also prove the existence of a discrete almost automorphic solution of the nonlinear
difference equation assuming that is discrete almost automorphic in for each ,
satisfies a global Lipschitz type condition, and takes values on .