Multiple Solutions for a Nonlinear Fractional Boundary Value Problem via Critical Point Theory

This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem D-T-(alpha)(a(x)D-0+(alpha)u(x)) = x is an element of [0, T], u(0) = u(T) = 0, where alpha is an element of (1/2, 1], a(x) is an element of L-infinity [0, T] with a(0) = essinf (x is an element of[0, T])a(x) > 0, DT-alpha and D0+alpha stand for the left and right Riemann- Liouville fractional derivatives of order alpha, respectively, and f : [0, T] x R -> R is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems.