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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 periodic solutions to some second-order nonautonomous differential equations


Author: Toka Diagana
Journal: Proc. Amer. Math. Soc. 140 (2012), 279-289
MSC (2010): Primary 39A24, 42A75, 35L10, 37L05, 34D09
Published electronically: June 1, 2011
MathSciNet review: 2833540
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Abstract: This paper is concerned with the existence of almost periodic mild solutions to some second-order equations. Using dichotomy tools and the Schauder fixed point theorem, the existence of almost periodic mild solutions to those second-order evolution equations is established. To illustrate our abstract results, the existence of almost periodic solutions to a damped second-order boundary value problem is also discussed.


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Additional Information

Toka Diagana
Affiliation: Department of Mathematics, Howard University, 2441 6th Street N.W., Washington, DC 20059
Email: tdiagana@howard.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10970-5
PII: S 0002-9939(2011)10970-5
Keywords: Schauder fixed point theorem, exponential dichotomy, almost periodic, second-order differential equation
Received by editor(s): November 17, 2010
Published electronically: June 1, 2011
Dedicated: In memory of my friend and colleague Cora Sadosky
Communicated by: Yingfei Yi
Article copyright: © Copyright 2011 American Mathematical Society