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

Abstract

This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: DT-αaxD0+αux=fx,ux,  x∈0,T, u0=uT=0, where α∈1/2,1, ax∈L∞0,T with a0=ess  infx∈0,Tax>0, DT-α and D0+α stand for the left and right Riemann-Liouville fractional derivatives of order α, respectively, and f:0,T×R→R is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems.