Massera-type theorem for the existence of C(n)-almost-periodic solutions for partial functional differential equations with infinite delay

In this paper, We Study the existence of C-(n)-almost-periodic solutions for partial functional differential equations with infinite delay. We assume that the undelayed part is not necessarily densely defined and satisfies the Hille-Yosida condition. We use the reduction principle developed recently in [M. Adimy, K. Ezzinbi, A. Ouhinou, Variation of constants formula and almost-periodic Solutions for some partial functional differential equations with infinite delay, Journal of Mathematical Analysis and Applications 317 (2006) 668-689] to prove the existence of a C-(n)-almost-periodic Solution when there is at least one bounded Solution ill R+. We give an application to the Lotka-Volterra model with diffusion. (C) 2007 Elsevier Ltd. All rights reserved.