GROUND STATES FOR FRACTIONAL SCHR?DINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL GROWTH

In this article, we study the following fractional Schr?dinger equation with electromagnetic fields and critical growth (-?)Asu + V(x)u = |u|2s*-2u + λf(x, |u|2)u, x ∈ RN,where(-?)Asis the fractional magnetic operator with 0 < s < 1, N > 2s, λ > 0, 2s*=2N/(N-2s),f is a continuous function, V ∈ C(RN, R) and A ∈ C(RN, RN) are the electric and magnetic potentials, respectively. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method.