Existence of weak solutions for a class of fractional Schrödinger equations with periodic potential

Abstract

We consider a time-independent fractional Schrödinger equation (−△)αu+V(x)u=f(x,u) in RN, u∈Hα(RN), where α∈(0,1), N>2α, V(x) is a periodic potential, f is superlinear and has a general subcritical growth. Based on a generalized linking theorem and a variant fountain theorem for strongly indefinite functional, we obtain a ground state solution and infinitely many solutions.