A note on periodic solutions of the delay differential equation
Author:
Jianshe Yu
Journal:
Proc. Amer. Math. Soc. 141 (2013), 12811288
MSC (2010):
Primary 34K13, 58E50
Published electronically:
August 10, 2012
MathSciNet review:
3008875
Fulltext PDF
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Abstract: Consider the delay differential equation , where is odd and satisfies for . When and exist, there is at least one KaplanYorke 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 KaplanYorke 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:
http://dx.doi.org/10.1090/S000299392012113863
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.
