Existence of L2‐Norms Constrained Solutions to Doubly Coupled Schrödinger Systems With Mass Supercritical Nonlinearity

We consider the existence of ‐norms constrained solution to Schrödinger systems with doubly coupled: where or 4, and are Lagrangian multipliers. When , we construct a linking structure for the case of small, and find a mountain pass structure for the case of large. In both cases, we use Ghoussoub's variational principle and delicate energy estimate to prove the existence result. After that, when , we show that for any , the constrained solutions exist.