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

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

Xin'an Hao1 , Lishan Liu1 and Yonghong Wu3

1Department of Mathematics, Qufu Normal University, Qufu 273165, Shandong, China
 3Department of Mathematics and Statistics, Curtin University of Technology, Perth 6845, WA, Australia

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.