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