Ground states and concentration phenomena for the fractional Schrodinger equation

We consider here solutions of the nonlinear fractional Schrodinger equation epsilon(2s) (-Delta)(s) u + V (x) u = u(p). 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 epsilon tends to zero. In addition, if the potential V is radial and radially decreasing, then the minimizer is unique provided epsilon is small.