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Applicable Analysis
An International Journal
Volume 84, 2005 - Issue 11
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Original Articles

Almost automorphic solutions of second order evolution equations

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Pages 1173-1184 | Received 01 Sep 2004, Published online: 04 Sep 2006
 

Abstract

This article is concerned with the existence of almost automorphic mild solutions to second order evolution equations of the form

where A generates a strongly continuous semigroup and f is an almost automorphic function. Using the notion of uniform spectrum of a function and the method of sums of commuting operators in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to (*) in terms of spectrum of A and uniform spectrum of f. Moreover, we study the nonlinear perturbation of this equation and obtain an extension of results by Diagana and N’Guérékata.

Notes

Additional information

Notes on contributors

Nguyen Van Minh Footnote§

Email: [email protected] Email: [email protected]

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