Boundary Value Problems
Volume 2010 (2010), Article ID 458015, 16 pages
doi:10.1155/2010/458015
Research Article

Existence of Positive Solutions of a Singular Nonlinear Boundary Value Problem

Ruyun Ma1 and Jiemei Li1,2

1College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China
2The School of Mathematics, Physics & Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 21 May 2010; Accepted 11 August 2010

Academic Editor: Vicentiu Radulescu

Copyright © 2010 Ruyun Ma and Jiemei Li. 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.

Abstract

We are concerned with the existence of positive solutions of singular second-order boundary value problem u″(t)+f(t,u(t))=0, t∈(0,1), u(0)=u(1)=0, which is not necessarily linearizable. Here, nonlinearity f is allowed to have singularities at t=0,1. The proof of our main result is based upon topological degree theory and global bifurcation techniques.