Almost Automorphic Solutions for Partial Functional Differential Equations with Infinite Delay

Abstract

In this work, we study the existence of almost automorphic 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 so-called reduction principle developed recently in [3], to show the existence of an almost automorphic solution under minimal condition. More precisely, the existence of an almost automorphic solution is proved when there is at least one bounded solution in the positive real half line. We give an application to the Lotka-Volterra model with diffusion.