Eberlein-weakly almost-periodic solutions of evolution equations in Banach spaces

Abstract

We study the asymptotic behavior of solutions to the---generally nonautonomous and nonlinear---Cauchy problem $$ u^{\prime}(t) \in A(t)u(t) + f(t), \ \ t \in \mathbb{R}^+ , \,\,\, u(0) = u_0. \tag {$CP_t$} $$ The emphasis is on almost-periodicity properties of the solution, in particular on weak almost periodicity (in the sense of Eberlein).