Almost automorphic and pseudo-almost automorphic mild solutions to an abstract differential equation in Banach spaces

In this paper we prove some existence results for almost automorphic and pseudo-almost automorphic mild solutions to a class of abstract differential equations in Banach spaces. The main technique is based on some composition theorems combined with the contraction mapping theorem. Finally, we presen...

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Bibliographic Details
Published in:Nonlinear analysis 2010-02, Vol.72 (3), p.1886-1894
Main Authors: Zhao, Zhi-Han, Chang, Yong-Kui, Nieto, Juan J.
Format: Article
Language:English
Subjects:
Almost automorphic
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematics
Neutral differential equations
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Pseudo-almost automorphic
Sciences and techniques of general use
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Summary:In this paper we prove some existence results for almost automorphic and pseudo-almost automorphic mild solutions to a class of abstract differential equations in Banach spaces. The main technique is based on some composition theorems combined with the contraction mapping theorem. Finally, we present an application to a semilinear partial differential equation with Dirichlet conditions.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.09.028