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PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

Part of: Qualitative theory

Published online by Cambridge University Press:  14 September 2010

JIFENG CHU  and
ZIHENG ZHANG
JIFENG CHU*
Affiliation:
Department of Mathematics, College of Science, Hohai University, Nanjing 210098, PR China (email: chujf05@mails.tsinghua.edu.cn)
ZIHENG ZHANG
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China (email: zhzh@mail.bnu.edu.cn)
*
✉For correspondence; e-mail: chujf05@mails.tsinghua.edu.cn
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Abstract

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In this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

Keywords

periodic solutionsingular differential equationSchauder’s fixed point theoremsign-changing potential

MSC classification

Secondary: 34C25: Periodic solutions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 3 , December 2010 , pp. 437 - 445
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

Jifeng Chu is supported by the National Natural Science Foundation of China (Grant No. 10801044), Jiangsu Natural Science Foundation (Grant No. BK2008356), the Program for New Century Excellent Talents in University (Grant No. NCET-10-0325) and the Fundamental Research Funds for the Central Universities.

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