Ground states of nonlinear fractional Schr\"odinger equation involving   critical growth
  In this paper, we are concerned with the ground state solutions of nonlinear fractional Schr\"odinger equation involving critical growth. Without Ambrosetti-Rabinowitz condition and monotonicity condition on the nonlinearity, we get the existence of ground state solutions of such equation when the potential $V(x)$ is not a constant and not radial. 
Hua Jin and Wenbin Liu
math.AP