Abstract
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 .
Highlights
The theory of difference equations has grown at an accelerated pace in the last decades
It occupies a central position in applicable analysis and plays an important role in mathematics as a whole
Advances in Difference Equations in 20, 21, and we give an application in the study of existence of discrete almost automorphic solutions of linear and nonlinear difference equations
Summary
The theory of difference equations has grown at an accelerated pace in the last decades. Several papers 10–16 are devoted to study existence of almost periodic solutions of difference equations. A class of functions which are more general than discrete almost periodic ones, were recently introduced in 17, Definition 2.6 in connection with the study of continuous almost automorphic bounded mild solutions of differential equations. Advances in Difference Equations in 20, 21 , and we give an application in the study of existence of discrete almost automorphic solutions of linear and nonlinear difference equations.
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