Ground state solution for differential equations with left and right fractional derivatives

Abstract

In this work, we study the existence of positive solutions for a class of fractional differential equation given by

D-t(infinity-infinity)alpha D(t)(alpha)u(t) + u(t) = f(t,u(t)),

u is an element of H-alpha (R),

where alpha is an element of(1/2,1),t is an element of R,u is an element of R,f is an element of C(R, R). Using the mountain pass theorem and comparison argument, we prove that ( 1) at least has one nontrivial solution