Almost Automorphy for Abstract Neutral Differential Equations Via Control Theory

In this paper we study the existence of almost automorphic solutions for a class of linear neutral functional differential equations with finite delay and values in a Banach space. We show that the existence of an almost automorphic mild solution is related to the approximate controllability of a distributed control system. We applied our results to establish the existence of an almost automorphic solution for a neutral wave equation with delay. © 2011 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.