Existence and Exponential Stability of Weighted Pseudo Almost Periodic Classical Solutions of Integro-Differential Equations with Analytic Semigroups

Abstract

In this paper, we investigate a class of integro-differential equations having analytic semigroups given by $$\begin{aligned} x'(t)=Ax(t)+f(t,x(t),Gx(t)). \end{aligned}$$ Our main results concern the existence, uniqueness and globally exponential stability of weighted pseudo-almost periodic classical solutions. An example is given to illustrate our results.