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(x(t)) + N(x(t)) + f(t), t is an element of R, where A : D(A) subset of 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 is an element of L-p(T, X). (C) 2011 Elsevier Ltd. All rights reserved.