Pseudo-almost-automorphic solutions to some neutral partial functional differential equations in Banach spaces

This work aims to investigate the existence and uniqueness of pseudo-almiost-automorphic Solutions for some neutral partial functional differential equations in Banach spaces. Recall that the new concept of pseudo-almost-automorphy generalizes the one of the pseudo-almost-periodicity and it has been recently introduced in the literature. Here we assume that the undelayed part is not necessarily densely defined and satisfies the well-known Hille-Yosida condition, the delayed parts are assumed to be Pseudo-almost-automorphic with respect to the first argument and Lipschitz continuous with respect to the second argument. (C) 2008 Elsevier Ltd. All rights reserved.