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 $H^1({\mathbb{R}}^n)$ space.

17 pages

Cited by in corpus (1)

• Optimal convergence rate of nonrelativistic limit for the nonlinear pseudo-relativistic equations