Ground states and concentration phenomena for the fractional Schrödinger equation

We consider here solutions of the nonlinear fractional Schrödinger equation We show that concentration points must be critical points for V. We also prove that if the potential V is coercive and has a unique global minimum, then ground states concentrate suitably at such a minimal point as ε tends to zero. In addition, if the potential V is radial and radially decreasing, then the minimizer is unique provided ε is small.