International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 5, Pages 361-365

Almost automorphic solutions of some differential equations in Banach spaces

Gaston Mandata N'Guerekata

Department of Mathematics, Morgan State University, Cold Spring Lane and Hillen Road, Baltimore, MD 21251, USA

Received 12 November 1997; Revised 2 March 1998

Copyright © 2000 Gaston Mandata N'Guerekata. 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.


We discuss the conditions under which bounded solutions of the evolution equation x(t)=Ax(t)+f(t) in a Banach space are almost automorphic whenever f(t) is almost automorphic and A generates a C0-group of strongly continuous operators. We also give a result for asymptotically almost automorphic solutions for the more general case of x(t)=Ax(t)+f(t,x(t)).