On the almost automorphy of bounded solutions of differential equations with piecewise constant argument

In this paper we give sufficient spectral conditions for the almost automorphy of bounded solutions to differential equations with piecewise constant argument of the form x (t) = Ax([t ]) + f (t), t ∈ R, where A is a bounded linear operator in X and f is an X-valued almost automorphic function. © 2006 Elsevier Inc. All rights reserved.