A note on periodic solutions of the delay differential equation

Author:
Jianshe Yu

Journal:
Proc. Amer. Math. Soc. **141** (2013), 1281-1288

MSC (2010):
Primary 34K13, 58E50

DOI:
https://doi.org/10.1090/S0002-9939-2012-11386-3

Published electronically:
August 10, 2012

MathSciNet review:
3008875

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider the delay differential equation , where is odd and satisfies for . When and exist, there is at least one Kaplan-Yorke periodic solution with period if . When this condition is not satisfied, we present several sufficient conditions on the existence/nonexistence of such periodic solutions. It is worthy of mention that some results are on the existence of at least two Kaplan-Yorke periodic solutions with period and in some cases we do not require the limits and/or to exist. Hence our results not only greatly improve but also complement existing ones. Moreover, some of the theoretical results are illustrated with examples.

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Additional Information

**Jianshe Yu**

Affiliation:
College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, People’s Republic of China

Email:
jsyu@gzhu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-2012-11386-3

Received by editor(s):
March 21, 2011

Received by editor(s) in revised form:
August 5, 2011

Published electronically:
August 10, 2012

Additional Notes:
This project was supported by the National Natural Science Foundation of China (11031002) and the grant DPFC (20104410110001).

Communicated by:
Yingfei Yi

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.