On the Almost Periodic Solutions of Differential Equations on Hilbert Spaces

Abstract

For the differential equation $u^{\prime }\left(t\right)=Au\left(t\right)+f\left(t\right)$, $t\ge 0$ on a Hilbert space $H$, we find the necessary and sufficient conditions that the above-mentioned equation has a unique almost periodic solution. Some applications are also given.