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.