Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 725494, 11 pages
Research Article

Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 13 September 2011; Revised 21 November 2011; Accepted 25 November 2011

Academic Editor: Gerhard-Wilhelm Weber

Copyright © 2011 Xiaoling Han and Hongliang Gao. 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.


By using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equation D0+αu(t)+λa(t)f(t,u(t))=0,  0<t<1,   u(0)=0,  u(1)=Σi=1αiu(ξi) are considered, where 1<α2 is a real number, λ is a positive parameter, D0+α is the standard Riemann-Liouville differentiation, and ξi(0,1), αi[0,) with Σi=1αiξiα-1<1, a(t)C([0,1],[0,)),  f(t,u)C([0,),[0,)).