Abstract and Applied Analysis
Volume 2012 (2012), Article ID 740760, 14 pages
http://dx.doi.org/10.1155/2012/740760
Research Article

Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations

Jing Wu1 and Xinguang Zhang2

1School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, Sichuan, China
2School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, Shandong, China

Received 22 October 2012; Accepted 19 November 2012

Academic Editor: Dragoş-Pătru Covei

Copyright © 2012 Jing Wu and Xinguang Zhang. 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 study the eigenvalue interval for the existence of positive solutions to a semipositone higher order fractional differential equation = =   where ,   , , , satisfying , is the standard Riemann-Liouville derivative, , and is allowed to be changing-sign. By using reducing order method, the eigenvalue interval of existence for positive solutions is obtained.