International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 5, Pages 361-365
doi:10.1155/S0161171200001988
Almost automorphic solutions to some differential equations in Banach spaces
Gaston Mandata N'Guérékata
Department of Mathematics, Morgan State University, Cold Spring Lane and Hillen Road, Baltimore, MD 21251, USA
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)).