Segregated solutions for some non-linear Schr\"odinger systems with critical growth

TL;DR

This paper demonstrates the existence of infinitely many positive, non-radial solutions for certain nonlinear Schrödinger systems with critical growth, under attractive or repulsive regimes with an external trapping potential.

Contribution

It introduces new methods to find multiple solutions for nonlinear Schrödinger systems with critical growth, including non-radial solutions in various regimes.

Findings

Existence of infinitely many positive non-radial solutions

Solutions found in both attractive and repulsive regimes

Application of external radial trapping potential

Abstract

We find infinitely many positive non-radial solutions for a system of Schr\"odinger equations with critical growth in a fully attractive or repulsive regime in presence of an external radial trapping potential.