Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations

In this paper, applying the theory of semigroups of operators to evolution family and Banach fixed point theorem, we prove the existence and uniqueness of an (a) almost automorphic (weighted pseudo almost automorphic) mild solution of the semilinear evolution equation x ′ ( t ) = A ( t ) x ( t ) + f...

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Bibliographic Details
Published inJournal of functional analysis Vol. 258; no. 1; pp. 196 - 207
Main Authors Liu, Jing-huai, Song, Xiao-qiu
Format Journal Article
LanguageEnglish
Published Elsevier Inc 2010
Subjects
Almost automorphic
Evolution family
Exponentially stable
Semilinear evolution equation
Weighted pseudo almost automorphic
Almost automorphic
Weighted pseudo almost automorphic
Semilinear evolution equation
Evolution family
Exponentially stable
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Summary:In this paper, applying the theory of semigroups of operators to evolution family and Banach fixed point theorem, we prove the existence and uniqueness of an (a) almost automorphic (weighted pseudo almost automorphic) mild solution of the semilinear evolution equation x ′ ( t ) = A ( t ) x ( t ) + f ( t , x ( t ) ) in Banach space under conditions.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2009.06.007