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Bulletin of the London Mathematical Society Advance Access originally published online on June 22, 2007
Bulletin of the London Mathematical Society 2007 39(4):653-660; doi:10.1112/blms/bdm040
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© 2007 London Mathematical Society

Applications of Schauder's fixed point theorem to singular differential equations

Jifeng Chu

Department of Mathematical Sciences
Tsinghua University
Beijing 100084
China
College of Science
Hohai University
Nanjing 210098
China
jifengchu{at}yahoo.com.cn

Pedro J. Torres

Departamento de Matemática Aplicada
Universidad de Granada
18071 Granada
Spain
ptorres{at}ugr.es

Received 19 August 2006. Revision received 29 December 2006.

In this paper, we study the existence of positive periodic solutions to second-order singular differential equations. The proof relies on Schauder's fixed point theorem. Our results show that in some situations weak singularities can help create periodic solutions, as pointed out by Torres [J. Differential Equations 232 (2007) 277–284].

Correspondence: chujf05{at}mails.tsinghua.edu.cn

2000 Mathematics Subject Classification 34B15, 34D20.

The first author is supported by the National Natural Science Foundation of China (Grant nos 10325102 and 10531010). The second author is supported by D.G.I. BFM2002-01308, Ministerio Ciencia y Tecnologi a, Spain.


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