Almost automorphic solutions for some partial functional differential equations

In this work, we study the existence of almost automorphic solutions for some partial functional differential equations. We prove that the existence of a bounded solution on R + implies the existence of an almost automorphic solution. Our results extend the classical known theorem by Bohr and Neugeb...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2007-04, Vol.328 (1), p.344-358
Main Authors: Ezzinbi, Khalil, N'Guérékata, Gaston Mandata
Format: Article
Language:English
Subjects:
Almost automorphic solution
Exact sciences and technology
Finite differences and functional equations
Hille–Yosida condition
Integral solution
Lotka–Volterra equation
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Semigroup
Spectral analysis
Variation of constants formula
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Summary:In this work, we study the existence of almost automorphic solutions for some partial functional differential equations. We prove that the existence of a bounded solution on R + implies the existence of an almost automorphic solution. Our results extend the classical known theorem by Bohr and Neugebauer on the existence of almost periodic solutions for inhomegeneous linear almost periodic differential equations. We give some applications to hyperbolic equations and Lotka–Volterra type equations used to describe the evolution of a single diffusive animal species.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2006.05.036