Almost Automorphic Solutions of Difference Equations
نویسندگان
چکیده
We study discrete almost automorphic functions sequences defined on the set of integers with values in a Banach space X. Given a bounded linear operator T defined on X and a discrete almost automorphic function f n , we give criteria for the existence of discrete almost automorphic solutions of the linear difference equation Δu n Tu n f n . We also prove the existence of a discrete almost automorphic solution of the nonlinear difference equation Δu n Tu n g n, u n assuming that g n, x is discrete almost automorphic in n for each x ∈ X, satisfies a global Lipschitz type condition, and takes values on X.
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