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.

Abstract

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=1∞αiu(ξi) are considered, where 1<α≤2 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=1∞αiξiα-1<1, a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,∞),[0,∞)).