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A NOTE ON PERIODIC SOLUTIONS OF A FORCED LIÉNARD-TYPE EQUATION

Part of: Qualitative theory

Published online by Cambridge University Press:  27 September 2010

LIE-HUI ZHANG  and
YONG WANG
LIE-HUI ZHANG
Affiliation:
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, PR China (email: zhangliehui@vip.163.com)
YONG WANG*
Affiliation:
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, PR China (email: zhangliehui@vip.163.com) School of Science, Southwest Petroleum University, Chengdu, Sichuan 610500, PR China (email: ywangsc@gmail.com)
*
✉For correspondence; e-mail: ywangsc@gmail.com
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Abstract

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Criteria for guaranteeing the existence, uniqueness and asymptotic stability (in the sense of Liapunov) of periodic solutions of a forced Liénard-type equation under certain assumptions are presented. These criteria are obtained by application of the Manásevich–Mawhin continuation theorem, Floquet theory, Liapunov stability theory and some analysis techniques. An example is provided to demonstrate the applicability of our results.

Keywords

Liénard equationperiodic solutionexistenceuniquenessstability

MSC classification

Secondary: 34C25: Periodic solutions
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 3 , January 2010 , pp. 350 - 368
Copyright
Copyright © Australian Mathematical Society 2010

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