Nonrelativistic limit of standing waves for pseudo-relativistic nonlinear Schr\"odinger equations

Abstract

In this paper we study standing waves for pseudo-relativistic nonlinear Schr\"odinger equations. In the first part we find ground state solutions. We also prove that they have one sign and are radially symmetric. The second part is devoted to take nonrelativistic limit of the ground state solutions in $H^1 (\mathbb{R}^n)$ space.