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

DOI:
https://doi.org/10.1090/S0002-9939-04-07556-2

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:
https://doi.org/10.1090/S0002-9939-04-07556-2

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