Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d ≥ 3 equations

This question had been clarified only in the d=2 equations case. For d≥3 equations, prior to the present paper, only very restrictive results were known, namely when the above system was a small perturbation of the super-symmetrical case λi≡λ and bij≡b. We treat the general case, uncovering in particular a much more complex and richer structure with respect to the d=2 case.