Abstract and Applied Analysis
Volume 5 (2001), Issue 4, Pages 245-263
doi:10.1155/S1085337501000367
Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations
Bernd Aulbach1
and Nguyen Van Minh2
1Department of Mathematics, University of Augsburg, Augsburg D-86135, Germany
2Department of Mathematics, The University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo 182-8585, Japan
Abstract
We study evolution semigroups associated with nonautonomous functional differential equations. In fact, we convert a given functional differential equation to an abstract autonomous evolution equation and then derive a representation theorem for the solutions of the underlying functional differential equation. The representation theorem is then used to study the boundedness and almost periodicity of solutions of a class of nonautonomous functional differential equations.