Exponential dichotomy and pseudo-almost automorphy for partial neutral functional differential equations

In this work, we study the existence and uniqueness of a pseudo-almost automorphic solution for some partial functional differential equations of neutral type. We assume that the undelayed part is not necessarily densely defined and satisfies the Hille-Yosida condition. The delay part is assumed to be pseudo-almost automrophic in time. We prove if the homogeneous linear equation has an exponential dichotomy, then the nonhomogeneous linear equation has a unique pseudo-almost automorphic solution. An application is given for some nonlinear equations. We present also a new concept of generalized pseudo-almost automorphy. (C) 2009 Elsevier Ltd. All rights reserved.