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This research aims to establish the existence of L2-norms constrained solutions in doubly coupled Schrödinger systems, focusing on nonlinearity factors.

April 25, 2026Mathematical Methods in the Applied Sciences0 citations

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

CDChonghao DengUniversity of International Business and Economics

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.

Abstract

ABSTRACT 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.

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

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