Periodic Solutions of Abstract Functional Differential Equations with Infinite Delay

We characterize the existence of periodic solutions for a class of abstract retarded functional differential equations with infinite delay. We apply our results to the nonlinear equation x?(t)=Ax(t)+L( xt)+N( xt)+f(t),t?R, where A:D(A)?X?X is a closed operator defined on a Banach space X, L is a bounded linear map, N:B?X is a continuous function defined on an appropriate phase space B and f? Lp(T,X). © 2011 Elsevier Ltd. All rights reserved.