Abstract and Applied Analysis
Volume 2012 (2012), Article ID 214042, 17 pages
http://dx.doi.org/10.1155/2012/214042
Research Article

Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity

Yongqing Wang,1 Lishan Liu,1,2 and Yonghong Wu2

1School of Mathematical Sciences, Qufu Normal University, Shandong, Qufu 273165, China
2Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia

Received 14 April 2012; Accepted 25 June 2012

Academic Editor: Bashir Ahmad

Copyright © 2012 Yongqing Wang 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

We discuss the existence of positive solutions to the following fractional m-point boundary value problem with changing sign nonlinearity D0+αu(t)+λf(t,u(t))=0,0<t<1,u(0)=0,D0+βu(1)=∑i=1m-2ηiD0+βu(ξi), where λ is a positive parameter, 1<α≤2, 0<β<α-1, 0<ξ1<⋯<ξm-2<1 with ∑i=1m-2ηiξiα-β-1<1, D0+α is the standard Riemann-Liouville derivative, f and may be singular at t=0 and/or t=1 and also may change sign. The work improves and generalizes some previous results.