Almost automorphic solutions of second order evolution equations

Authors: Liu, James¹; N'Guérékata, Gaston M.²; Minh, Nguyen Van¹

Source: Applicable Analysis, Volume 84, Number 11, November 2005 , pp. 1173-1184(12)

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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.

Keywords: Analytic semigroup; Almost automorphic solution; Uniform spectrum; Sums of commuting operators; 1991 Mathematics Subject Classification: Primary:; Secondary: 43A60

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00036810410001724372

Affiliations: 1: Department of Mathematics, James Madison University, Harrisonburg VA 22801 2: Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA

Publication date: 2005-11-01

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