Copyright © 2012 Ge Bin. 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 multiplicity of solutions for the following fractional boundary value problem: where and are the left and right Riemann-Liouville fractional integrals of order , respectively, is a real number, is a given function, and is the gradient of at . The approach used in this paper is the variational method. More precisely, the Weierstrass theorem and mountain pass theorem are used to prove the existence of at least two nontrivial solutions.