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

Recommended by Ivan Kiguradze

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.