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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Almost automorphic solutions of semilinear evolution equations


Authors: Jerome A. Goldstein and Gaston M. N'Guérékata
Journal: Proc. Amer. Math. Soc. 133 (2005), 2401-2408
MSC (2000): Primary 34A05, 34K05, 47D60, 34G20
Published electronically: March 4, 2005
MathSciNet review: 2138883
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Abstract | References | Similar Articles | Additional Information

Abstract: We are concerned with the semilinear differential equation in a Banach space $\mathbb{X} $,

\begin{displaymath}x'(t)=Ax(t)+F(t,x(t)),\; t\in \mathbb{R}\, ,\end{displaymath}

where $A$ generates an exponentially stable $C_0$-semigroup and $F(t,x): \mathbb{R}\times \mathbb{X}\to \mathbb{X} $is a function of the form $F(t,x)=P(t)Q(x)$. Under appropriate conditions on $P$ and $Q$, and using the Schauder fixed point theorem, we prove the existence of an almost automorphic mild solution to the above equation.


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Additional Information

Jerome A. Goldstein
Affiliation: Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152-3240
Email: jgoldste@memphis.edu

Gaston M. N'Guérékata
Affiliation: Department of Mathematics, Morgan State University, Baltimore, Maryland 21251
Email: gnguerek@jewel.morgan.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07790-7
PII: S 0002-9939(05)07790-7
Received by editor(s): February 11, 2004
Received by editor(s) in revised form: April 12, 2004
Published electronically: March 4, 2005
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2005 American Mathematical Society