Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations

Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations

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 differentia...

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Main Authors: Bernd Aulbach, Nguyen Van Minh
Format: Article
Language:English
Published: Hindawi Limited 2000-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/S1085337501000367
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spelling doaj-28c8c372e10e4594a2840413dff826442020-11-24T21:33:14ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092000-01-015424526310.1155/S1085337501000367Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equationsBernd Aulbach0Nguyen Van Minh1Department of Mathematics, University of Augsburg, Augsburg D-86135, GermanyDepartment of Mathematics, The University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo 182-8585, JapanWe 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.http://dx.doi.org/10.1155/S1085337501000367
collection DOAJ
language English
format Article
sources DOAJ
author Bernd Aulbach
Nguyen Van Minh
spellingShingle Bernd Aulbach
Nguyen Van Minh
Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations
Abstract and Applied Analysis
author_facet Bernd Aulbach
Nguyen Van Minh
author_sort Bernd Aulbach
title Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations
title_short Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations
title_full Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations
title_fullStr Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations
title_full_unstemmed Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations
title_sort bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2000-01-01
description 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.
url http://dx.doi.org/10.1155/S1085337501000367
work_keys_str_mv AT berndaulbach boundedandalmostperiodicsolutionsandevolutionsemigroupsassociatedwithnonautonomousfunctionaldifferentialequations
AT nguyenvanminh boundedandalmostperiodicsolutionsandevolutionsemigroupsassociatedwithnonautonomousfunctionaldifferentialequations
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