Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 69073, 12 pages

Positive solutions of three-point boundary value problems for higher-order p-Laplacian with infinitely many singularities

Fuyi Xu,1 Yonghong Wu,2 Lishan Liu,3 and Yunming Zhou1

1School of Mathematics and Information Science, Shandong University of Technology, Zibo 255049, Shandong, China
2Department of Mathematics and Statistics, Curtin University of Technology, Perth 6845, WA, Australia
3Department of Mathematics, Qufu Normal University, Qufu 273165, Shandong, China

Received 15 March 2006; Accepted 10 May 2006

Copyright © 2006 Fuyi Xu 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.


We study a three-point nonlinear boundary value problem with higher-order p-Laplacian. We show that there exist countable many positive solutions by using the fixed point index theorem for operators in a cone.