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

In this paper, we study the existence of C(n)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)C(n)-almost- periodic solution when there is at least one bounded solution in R+R+. We give an application to the Lotka–Volterra model with diffusion.