Bulletin of the Australian Mathematical Society

Research Article

PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

JIFENG CHUa1 c1 and ZIHENG ZHANGa2

a1 Department of Mathematics, College of Science, Hohai University, Nanjing 210098, PR China (email: chujf05@mails.tsinghua.edu.cn)

a2 School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China (email: zhzh@mail.bnu.edu.cn)

Abstract

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.

(Received May 03 2009)

2000 Mathematics subject classification

  • primary 34C25; secondary 34D20

Keywords and phrases

  • periodic solution;
  • singular differential equation;
  • Schauder’s fixed point theorem;
  • sign-changing potential

Correspondence:

c1 For correspondence; e-mail: chujf05@mails.tsinghua.edu.cn

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.