Pseudo almost periodic solutions of class r for neutral partial functional differential equations

The aim of this work is to investigate the existence and uniqueness of pseudo almost periodic solutions of class r for some neutral partial functional differential equations in a Banach space when the delay is distributed using the variation of constants formula and the spectral decomposition of the phase space developed in Adimy et al. (Can Appl Math Q, 9(1):1-34, 2001). Here we assume that the undelayed part is not necessarily densely defined and satisfies the well-known Hille-Yosida condition, the delayed part are assumed to be pseudo almost periodic with respect to the first argument and Lipschitz continuous with respect to the second argument. © 2012 African Mathematical Union and Springer-Verlag.