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Almost automorphic solutions of evolution equations
Author(s):
Toka
Diagana;
Gaston
Nguerekata;
Nguyen
Van
Minh
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3289-3298.
MSC (2000):
Primary 34G10;
Secondary 43A60
Posted:
June 18, 2004
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References |
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Additional information
Abstract:
This paper is concerned with the existence of almost automorphic mild solutions to equations of the form
where  generates a holomorphic semigroup and  is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used 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 the imaginary spectrum of  and the uniform spectrum of  .
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Additional Information:
Toka
Diagana
Affiliation:
Department of Mathematics, Howard University, 2441 6th Street N.W., Washington D.C. 20059
Email:
tdiagana@howard.edu
Gaston
Nguerekata
Affiliation:
Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, Maryland 21251
Email:
gnguerek@jewel.morgan.edu
Nguyen
Van
Minh
Affiliation:
Department of Mathematics, Hanoi University of Science, Khoa Toan, Dai Hoc Khoa Hoc Tu Nhien, 334 Nguyen Trai, Hanoi, Vietnam
Address at time of publication:
Department of Mathematics, State University of West Georgia, Carrollton, Georgia 30118
Email:
nvminh@netnam.vn, ngvminh@yahoo.com
DOI:
10.1090/S0002-9939-04-07571-9
PII:
S 0002-9939(04)07571-9
Keywords:
Analytic semigroup,
almost automorphic solution,
uniform spectrum,
sums of commuting operators
Received by editor(s):
July 16, 2003
Posted:
June 18, 2004
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2004,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article T. Diagana and G. M. N'Guerekata, On Some Perturbations of Some Differential Equations, Comment. Math. (2) XLIII (2003), 201-206.
T. Diagana and G. M. N'Guerekata, Some Extensions of the Bohr-Neugebauer-N'Guerekata Theorem, J. of Anal. Appl. (1) 4 (2004), 1-10.
T. Diagana, Some Remarks on Some Second-order Hyperbolic Differential Equations, Semigroup Forum 68 (2004), 357-364.
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