Almost Automorphic Solutions of Difference Equations. (22nd June 2009) - Araya, Daniela; Castro, Rodrigo; Lizama, Carlos
Abstract : We study discrete almost automorphic functions (sequences) defined on the set of integers with values in a Banach spaceX . Given a bounded linear operatorT defined onX and a discrete almost automorphic functionf ( n ), we give criteria for the existence of discrete almost automorphic solutions of the linear difference equationΔ u ( n ) = T u ( n ) + f ( n ) . We also prove the existence of a discrete almost automorphic solution of the nonlinear difference equationΔ u ( n ) = T u ( n ) + g ( n, u ( n ) ) assuming thatg ( n, x ) is discrete almost automorphic inn for eachx ∈ X, satisfies a global Lipschitz type condition, and takes values onX .