Ground-states for systems of MM coupled semilinear Schrödinger equations with attraction–repulsion effects: Characterization and perturbation results

We focus on the study of ground-states for the system of MM coupled semilinear Schrödinger equations with power-type nonlinearities and couplings. We extend the characterization result in Correia (2016) 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.