Abstract and Applied Analysis
Volume 5 (2000), Issue 4, Pages 245-263
Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations
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
Received 8 September 2000
Copyright © 2000 Bernd Aulbach and Nguyen Van Minh. 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 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.