Ground-states for systems of $M$ coupled semilinear Schr\"odinger equations with attraction-repulsion effects: characterization and perturbation results

TL;DR

This paper characterizes ground-states for coupled semilinear Schrödinger systems with attraction and repulsion effects, extending previous results and providing conditions for their existence and behavior.

Contribution

It extends the characterization of ground-states to systems with combined attraction and repulsion, including perturbation and classification results for out-of-phase components.

Findings

Extended characterization of ground-states with attraction-repulsion effects.

Derived conditions for existence of nontrivial ground-states.

Provided perturbation and classification results for complex systems.

Abstract

We focus on the study of ground-states for the system of $M$ coupled semilinear Schr\"odinger equations with power-type nonlinearities and couplings. We extend the characterization result from a previous work (arXiv:1410.7993) to the case where both attraction and repulsion are present and cannot be studied separately. Furthermore, we derive some perturbation and classification results to study the general system where components may be out of phase. In particular, we present several conditions to the existence of nontrivial ground-states.