Positive ground states for a subcritical and critical coupled system involving Kirchhoff-Schr\"odinger equations

TL;DR

This paper establishes the existence of positive ground state solutions for subcritical and critical coupled Kirchhoff-Schrödinger systems using variational methods, and also proves nonexistence in certain cases.

Contribution

It introduces a variational approach to find ground states for coupled Kirchhoff-Schrödinger systems in both subcritical and critical regimes, including nonexistence results.

Findings

Existence of positive ground states in subcritical and critical cases

Application of Nehari manifold minimization technique

Nonexistence results via Pohozaev identity

Abstract

In this paper we prove the existence of positive ground state solution for a class of linearly coupled systems involving Kirchhoff-Schr\"odinger equations. We study the subcritical and critical case. Our approach is variational and based on minimization technique over the Nehari manifold. We also obtain a nonexistence result using a Pohozaev identity type.