International Journal of Differential Equations
Volume 2009 (2009), Article ID 575939, 11 pages
doi:10.1155/2009/575939
Research Article

On the Almost Periodic Solutions of Differential Equations on Hilbert Spaces

Nguyen Thanh Lan

Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA

Received 18 January 2009; Accepted 13 April 2009

Academic Editor: Toka Diagana

Copyright © 2009 Nguyen Thanh Lan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.