Boundary Value Problems
Volume 2008 (2008), Article ID 728603, 8 pages
doi:10.1155/2008/728603
Research Article

Multiple Positive Solutions for Singular Quasilinear Multipoint BVPs with the First-Order Derivative

Weihua Jiang,1,2 Bin Wang,3 and Yanping Guo1

1College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018 Hebei, China
2College of Mathematics and Science of Information, Hebei Normal University, Shijiazhuang, 050016 Hebei, China
3Department of Basic Courses, Hebei Professional and Technological College of Chemical and Pharmaceutical Engineering, Shijiazhuang, 050031 Hebei, China

Received 28 November 2007; Accepted 1 April 2008

Academic Editor: Wenming Zou

Copyright © 2008 Weihua Jiang 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

The existence of at least three positive solutions for differential equation (ϕp(u′(t)))′+g(t)f(t,u(t),u′(t))=0, under one of the following boundary conditions: u(0)=∑i=1m−2aiu(ξi), φp(u′(1))=∑i=1m−2biφp(u′(ξi)) or φp(u′(0))=∑i=1m−2aiφp(u′(ξi)), u(1)=∑i=1m−2biu(ξi) is obtained by using the H. Amann fixed point theorem, where φp(s)=|s|p−2s, p>1, 0<ξ1<ξ2<⋯<ξm−2<1, ai>0, bi>0, 0<∑i=1m−2ai<1, 0<∑i=1m−2bi<1. The interesting thing is that g(t) may be singular at any point of [0,1] and f may be noncontinuous.