Segregated solutions for nonlinear Schr\"odinger systems with weak interspecies forces

TL;DR

This paper discovers positive non-radial solutions for a nonlinear Schrödinger system under weak interspecies forces, considering attractive or repulsive regimes with external potentials that have extremal points at infinity.

Contribution

It introduces new solutions for Schrödinger systems with weak interspecies interactions and external potentials with specific asymptotic behaviors.

Findings

Existence of positive non-radial solutions

Solutions under weak attractive or repulsive regimes

Analysis of external potentials with extremal points at infinity

Abstract

We find positive non-radial solutions for a system of Schr\"odinger equations in a weak fully attractive or repulsive regime in presence of an external radial trapping potential that exhibits a maximum or a minimum at infinity.