Massera problem for non-autonomous retarded differential equations

In this paper, under Acquistapace-Terreni conditions, we study the existence of periodic solutions for some non-autonomous semilinear partial functional differential equation with delay. We assume that the linear part is non-densely defined. The delayed part is assumed to be omega-periodic with respect to the first argument. Using a fixed point theorem for multivalued mapping, some sufficient conditions are given, to prove the existence of periodic solutions. An example is shown to illustrate our results. (C) 2013 Elsevier Inc. All rights reserved.