Characterization of ground-states for a system of M coupled semilinear Schrödinger equations and applications

We focus on the study of ground-states for the system of M   coupled semilinear Schrödinger equations with power-type nonlinearities and couplings. General results regarding existence and characterization are derived using a variational approach. We show the usefulness of such a characterization in several particular cases, including those for which uniqueness of ground-states is already known. Finally, we apply the results to find the optimal constant for the vector-valued Gagliardo–Nirenberg inequality and we study global existence, L2L2-concentration phenomena and blowup profile for the evolution system in the L2L2-critical power case.