Nonrelativistic limit of standing waves for pseudo-relativistic nonlinear Schrödinger equations

Abstract

In this paper, we study standing waves for pseudo-relativistic nonlinear Schrödinger 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 H1(ℝn) space.