Ground states and concentration phenomena for the fractional Schrodinger equation

Abstract

We consider here solutions of the nonlinear fractional Schr¨odinger equation ε2s(− )su + V (x)u = up. 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