(ω, c)-Periodic Mild Solutions to Non-Autonomous Abstract Differential Equations

We investigate the semi-linear, non-autonomous, first-order abstract differential equation x '(t)=A(t)x(t)+f(t,x(t),phi[alpha(t,x(t))]),t is an element of R. We obtain results on existence and uniqueness of (omega,c)-periodic (second-kind periodic) mild solutions, assuming that A(t) satisfies the so-called Acquistapace-Terreni conditions and the homogeneous associated problem has an integrable dichotomy. A new composition theorem and further regularity theorems are given.