International Journal of Mathematics and Mathematical Sciences 
Volume 23 (2000), Issue 5, Pages 361-365
doi:10.1155/S0161171200001988

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

Abstract

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)).