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Periodic solutions in periodic state-dependent delay equations and population models
Author(s):
Yongkun
Li;
Yang
Kuang
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1345-1353.
MSC (2000):
Primary 34K13;
Secondary 34K20, 92D25
Posted:
December 27, 2001
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Abstract:
Sufficient and realistic conditions are obtained for the existence of positive periodic solutions in periodic equations with state-dependent delay. The method involves the application of the coincidence degree theorem and estimations of uniform upper bounds on solutions. Applications of these results to some population models are presented. These application results indicate that seasonal effects on population models often lead to synchronous solutions. In addition, we may conclude that when both seasonality and time delay are present and deserve consideration, the seasonality is often the generating force for the often observed oscillatory behavior in population densities.
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Additional Information:
Yongkun
Li
Affiliation:
Department of Mathematics, Yunnan University, Kunming, People's Republic of China
Yang
Kuang
Affiliation:
Department of Mathematics, Arizona State University, Tempe, Arizona 85287
Email:
kuang@asu.edu
DOI:
10.1090/S0002-9939-01-06444-9
PII:
S 0002-9939(01)06444-9
Keywords:
Coincidence degree,
periodic solution,
delay equation,
state-dependent delay,
population model
Received by editor(s):
July 1, 2000
Posted:
December 27, 2001
Additional Notes:
The second author's research was partially supported by NSF Grant DMS-0077790
Communicated by:
Suncica Canic
Copyright of article:
Copyright
2001,
American Mathematical Society
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