Almost Automorphic Solutions of Difference Equations. (22nd June 2009)

• Record Type: Journal Article
• Authors: Araya, Daniela; Castro, Rodrigo; Lizama, Carlos
• Other Names: Benchohra Mouffak Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2009(2009)
• Publication Date: 2009-06-22
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2009/591380
• Languages: English
• ISSNs: 1687-1847

Abstract

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 .