Periodic solutions in periodic state-dependent delay equations and population models

Authors:
Yongkun Li and Yang Kuang

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1345-1353

MSC (2000):
Primary 34K13; Secondary 34K20, 92D25

Published electronically:
December 27, 2001

MathSciNet review:
1879956

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-01-06444-9

Keywords:
Coincidence degree,
periodic solution,
delay equation,
state-dependent delay,
population model

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

Article copyright:
© Copyright 2001
American Mathematical Society