On the Almost Periodic Solutions of Differential Equations on Hilbert Spaces

Abstract

For the differential equation 𝑢(𝑡)=𝐴𝑢(𝑡)+𝑓(𝑡), 𝑡≥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.