# Construction of a solution for the two-component radial Gross-Pitaevskii system with a large coupling parameter

## TL;DR

This paper constructs solutions for a two-component radial Gross-Pitaevskii system with large coupling, showing convergence to a segregated profile and establishing solution persistence under symmetry and non-degeneracy assumptions.

## Contribution

It provides a novel perturbation method to prove the existence of solutions in the radial case for strongly coupled systems, extending understanding of Bose-Einstein condensates.

## Key findings

- Solutions converge to a segregated profile as coupling increases
- Persistence of solutions under radial symmetry and non-degeneracy
- Establishment of a perturbation approach for large coupling regimes

## Abstract

We consider strongly coupled competitive elliptic systems that arise in the study of two-component Bose-Einstein condensates. As the coupling parameter tends to infinity, solutions that remain uniformly bounded are known to converge to a segregated limiting profile, with the difference of its components satisfying a limit scalar PDE. In the case of radial symmetry, under natural non-degeneracy assumptions on a solution of the limit problem, we establish by a perturbation argument its persistence as a solution to the elliptic system.