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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Convergence in almost periodic cooperative systems with a first integral


Authors: Wenxian Shen and Xiao-Qiang Zhao
Journal: Proc. Amer. Math. Soc. 133 (2005), 203-212
MSC (2000): Primary 34C12, 34C27, 37B55
Published electronically: June 18, 2004
MathSciNet review: 2085171
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Abstract: This paper is to investigate the asymptotic dynamics in almost periodic cooperative systems with a first integral. By appealing to the theory of skew-product semiflows we establish the asymptotic almost periodicity of bounded solutions to such systems, which extends the existing convergence results for time independent and periodic cooperative systems with a first integral and proves a conjecture of B. Tang, Y. Kuang and H. Smith in SIAM J. Math. Anal., 24 (1993), 1331-1339.


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Additional Information

Wenxian Shen
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849
Email: ws@math.auburn.edu

Xiao-Qiang Zhao
Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 5S7
Email: xzhao@math.mun.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07556-2
PII: S 0002-9939(04)07556-2
Keywords: Cooperative systems, first integral, almost periodic solutions, skew-product semiflows
Received by editor(s): June 17, 2003
Received by editor(s) in revised form: September 24, 2003
Published electronically: June 18, 2004
Additional Notes: The first author’s research was supported in part by NSF grant DMS-0103381
The second author’s research was supported in part by the NSERC of Canada
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2004 American Mathematical Society