Ground and bound state solutions for a Schr\"odinger system with linear and nonlinear couplings in $\mathbb{R}^N$

TL;DR

This paper investigates the existence of ground and bound state solutions for a coupled Schrödinger system with linear and nonlinear interactions in multi-dimensional space, employing concentration compactness methods.

Contribution

It introduces new existence results for solutions of coupled Schrödinger systems, including the limit case, under specific assumptions.

Findings

Existence of ground state solutions established.

Existence of bound state solutions demonstrated.

Results are novel even for the limit system.

Abstract

We study the existence of ground and bound state solutions for a system of coupled Schr\"odinger equations with linear and nonlinear couplings in $\mathbb{R}^N$. By studying the limit system and using concentration compactness arguments, we prove the existence of ground and bound state solutions under suitable assumptions. Our results are new even for the limit system.