ftp ejde.math.txstate.edu (login: ftp) 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) + f(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 f, g are given functions. 1