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WEIGHTED PSEUDO-ALMOST PERIODIC SOLUTIONS FOR SOME ABSTRACT DIFFERENTIAL EQUATIONS WITH UNIFORM CONTINUITY

Part of: Qualitative theory Harmonic analysis in one variable

Published online by Cambridge University Press:  13 October 2010

LI-LI ZHANG  and
HONG-XU LI
LI-LI ZHANG
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China (email: zllyou@126.com)
HONG-XU LI*
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China (email: hoxuli@sohu.com)
*
✉For correspondence; e-mail: hoxuli@sohu.com
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Abstract

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In this work, we give some theorems on (mild) weighted pseudo-almost periodic solutions for some abstract semilinear differential equations with uniform continuity. To facilitate this we give a new composition theorem of weighted pseudo-almost periodic functions. Our composition theorem improves the known one by making use of a uniform continuity condition instead of the Lipschitz condition.

Keywords

almost periodicweighted pseudo-almost periodicuniform continuityfixed pointC0-semigroup

MSC classification

Secondary: 34C27: Almost and pseudo-almost periodic solutions 42A75: Classical almost periodic functions, mean periodic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 3 , December 2010 , pp. 424 - 436
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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