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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 603203, 8 pages
Research Article

Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter

Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, Hebei 050003, China

Received 10 June 2014; Accepted 30 July 2014; Published 12 August 2014

Academic Editor: Alberto Cabada

Copyright © 2014 Jian Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the following second-order three-point boundary value problem , , , , where , , , and is a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and then some useful properties of Green’s function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of by means of the fixed point index theory.