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 $$ frac{d}{dt} (x(t)+g(t,x(t))=Ax(t)+f(t,Bx(t)), $$ 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.

Keywords

• Almost periodic
• asymptotically almost periodic
• semigroup of linear operators.