On Schr\"odinger Systems with Local and Nonlocal Nonlinearities - Part II

TL;DR

This paper investigates special solutions of a nonlinear Schr"odinger system without a magnetic field, focusing on existence and symmetry properties of ground states, extending prior work on the same system.

Contribution

It establishes the existence and symmetry properties of ground state solutions for Schr"odinger systems with local and nonlocal nonlinearities when the magnetic field is absent.

Findings

Existence of special solutions confirmed.

Ground states exhibit certain symmetry properties.

Results extend previous analysis to non-magnetic cases.

Abstract

In this second part, we establish the existence of special solutions of the nonlinear Schr\"odinger system studied in the first part when the diamagnetic field is nul. We also prove some symmetry properties of these ground states solutions.