Periodic solutions in periodic state-dependent delay equations and population models
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- by Yongkun Li and Yang Kuang PDF
- Proc. Amer. Math. Soc. 130 (2002), 1345-1353 Request permission
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.References
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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
- Received by editor(s): July 1, 2000
- Published electronically: December 27, 2001
- Additional Notes: The second author’s research was partially supported by NSF Grant DMS-0077790
- Communicated by: Suncica Canic
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1345-1353
- MSC (2000): Primary 34K13; Secondary 34K20, 92D25
- DOI: https://doi.org/10.1090/S0002-9939-01-06444-9
- MathSciNet review: 1879956