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.

arXiv comment17 pages

References in corpus (3)

• Boson Stars as Solitary Waves
• Well-Posedness for Semi-Relativistic Hartree Equations of Critical Type
• Blow-Up for Nonlinear Wave Equations describing Boson Stars

Cited by in corpus (1)

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