Boundary Value Problems
Volume 2007 (2007), Article ID 74517, 10 pages
doi:10.1155/2007/74517
Research Article

Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems

Xin'an Hao,1 Lishan Liu,1,2 and Yonghong Wu2

1Department of Mathematics, Qufu Normal University, Qufu 273165, Shandong, China
2Department of Mathematics and Statistics, Curtin University of Technology, Perth 6845, WA, Australia

Received 23 June 2006; Revised 16 January 2007; Accepted 26 January 2007

Academic Editor: Ivan Kiguradze

Copyright © 2007 Xin'an Hao 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.

Abstract

We study the existence and multiplicity of positive solutions for a class of nth-order singular nonlocal boundary value problemsu(n)(t)+a(t)f(t,u)=0, t∈(0,1), u(0)=0, u'(0)=0, …,u(n−2)(0)=0, αu(η)=u(1), where 0<η<1,  0<αηn−1 <1. The singularity may appear at t=0 and/or t=1. The Krasnosel'skii-Guo theorem on cone expansion and compression is used in this study. The main results improve and generalize the existing results.