Ground states for fractional Schrödinger equations with critical growth

Abstract

In this paper, we study the following critical fractional Schrödinger equation: (−Δ)su+V(x)u=|u|2s*−2u+λf(x,u), x∈RN, where λ > 0, 0 < s < 1, N > 2s, 2s*=2NN−2s, (−Δ)s denotes the fractional Laplacian of order s, and f is a continuous superlinear but subcritical function. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by the Nehari method.