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 | References | Similar Articles | Additional Information

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

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