Asymptotically almost periodic and almost periodic solutions for a class of evolution equations

Abstract

In this paper we study the existence of asymptotically almost periodic and almost periodic solutions for the partial evolution equation d/ dt (x(t) + g(t, x(t)) = Ax(t) + ƒ(t, Bx(t)), where A is the infinitesimal generator of an analytic semigroup on a Banach space X, B is a closed linear operator, and ƒ, g are given functions.