Boundary Value Problems
Volume 2010 (2010), Article ID 862079, 23 pages
doi:10.1155/2010/862079
Research Article

Positive Solutions for Fourth-Order Singular p-Laplacian Differential Equations with Integral Boundary Conditions

Xingqiu Zhang1,2 and Yujun Cui3

1Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
2Department of Mathematics, Liaocheng University, Liaocheng, Shandong 252059, China
3Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao 266510, China

Received 7 April 2010; Accepted 12 August 2010

Academic Editor: Claudianor O. Alves

Copyright © 2010 Xingqiu Zhang and Yujun Cui. 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

By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo-C3[0,1] as well as C2[0,1] positive solutions for fourth-order singular p-Laplacian differential equations with integral boundary conditions. Our nonlinearity f may be singular at t=0, t=1, and u=0. The dual results for the other integral boundary condition are also given.