Abstract and Applied Analysis
Volume 2010 (2010), Article ID 971824, 12 pages
doi:10.1155/2010/971824
Research Article

Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator

Jinhua Wang and Hongjun Xiang

Department of Mathematics, Xiangnan University, Chenzhou 423000, China

Received 24 May 2010; Accepted 25 August 2010

Academic Editor: Paul Eloe

Copyright © 2010 Jinhua Wang and Hongjun Xiang. 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 upper and lower solutions method is used to study the p-Laplacian fractional boundary value problem D0+γ(ϕp(D0+αu(t)))=f(t,u(t)), 0<t<1, u(0)=0, u(1)=au(ξ), D0+αu(0)=0, and D0+αu(1)=bD0+αu(η), where 1<α,γ⩽2,0⩽a,b⩽1,0<ξ,η<1. Some new results on the existence of at least one positive solution are obtained. It is valuable to point out that the nonlinearity f can be singular at t=0,1 or u=0.