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

Key Points

• This research aims to establish the existence of L2-norms constrained solutions in doubly coupled Schrödinger systems, focusing on nonlinearity factors.
• Constructed linking and mountain pass structures based on the size of parameters.
• Utilized Ghoussoub's variational principle along with delicate energy estimates.
• Proved the existence results for specific conditions of Lagrangian multipliers.
• Constrained solutions were shown to exist for the case of small parameters.
• In the case of large parameters, a mountain pass structure proved the existence of solutions.
• Additionally, for any defined value of parameters, constrained solutions were established.