Existence of globally attracting almost automorphic solutions to some nonautonomous higher-order difference equations

In this paper we introduce a new theory for asymptotically almost automorphic sequences on Z+Z+ which is a natural generalization of the concept of asymptotically almost periodicity for sequences due to Ky Fan. We next make extensive use of such a newly introduced concept as well as discrete dichotomy techniques to study and establish the existence of globally attracting almost automorphic solutions to some higher-order nonautonomous difference equations.