Open Access Research

Existence of positive solutions to periodic boundary value problems with sign-changing Green's function

Shengren Zhong1 and Yukun An2*

Author Affiliations

1 Department of Engineering Technology, Wuwei Occupational College Wuwei, 733000, Gansu, PR China

2 Department of Mathematics, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, PR China

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Boundary Value Problems 2011, 2011:8 doi:10.1186/1687-2770-2011-8

Published: 27 July 2011

Abstract

This paper deals with the periodic boundary value problems

where is a constant and in which case the associated Green's function may changes sign. The existence result of positive solutions is established by using the fixed point index theory of cone mapping.

Keywords:
periodic boundary value problem; positive solution; sign-changing Green's function; cone; fixed point theorem