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Open Access Research

Multiplicity of positive solutions to second-order singular differential equations with a parameter

Shengjun Li12*, Fang-fang Liao3 and Hailong Zhu4

Author Affiliations

1 College of Science, Hohai University, Nanjing, 210098, China

2 Department of Mathematics, Hainan University, Haikou, 570228, China

3 Nanjing College of Information Technology, Nanjing, 210046, China

4 School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, 233030, China

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Boundary Value Problems 2014, 2014:115  doi:10.1186/1687-2770-2014-115

Published: 14 May 2014

Abstract

We study the existence and multiplicity of positive periodic solutions for second-order nonlinear damped differential equations by combing the analysis of positiveness of the Green function for a linear damped equation. Our nonlinearity may be singular in its dependent variable. The proof of the main result relies on the Guo-Krasnosel’skii fixed point theorem on compression and expansion of cones.

MSC: 34B16, 34C25.

Keywords:
positive solutions; singular; Guo-Krasnosel’skii fixed point theorem