Abstract and Applied Analysis

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Abstract and Applied Analysis / 2000 / Article

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Volume 5 |Article ID 405039 | 19 pages | https://doi.org/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

Received08 Sep 2000

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.

Copyright © 2000 Hindawi Publishing Corporation. 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.

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