We consider the system of coupled elliptic equations−Δu−λ1u=μ1u3+βuv2−Δv−λ2v=μ2v3+βu2vin R3, and study the existence of positive solutions satisfying the additional condition∫R3u2=a12and∫R3v2=a22. Assuming that a1,a2,μ1,μ2 are positive fixed quantities, we prove existence results for different ranges of the coupling parameter β>0. The extension to systems with an arbitrary number of components is discussed, as well as the orbital stability of the corresponding standing waves for the related Schrödinger systems.

Normalized solutions for a system of coupled cubic Schrödinger equations on R3

SOAVE, NICOLA
2016

Abstract

We consider the system of coupled elliptic equations−Δu−λ1u=μ1u3+βuv2−Δv−λ2v=μ2v3+βu2vin R3, and study the existence of positive solutions satisfying the additional condition∫R3u2=a12and∫R3v2=a22. Assuming that a1,a2,μ1,μ2 are positive fixed quantities, we prove existence results for different ranges of the coupling parameter β>0. The extension to systems with an arbitrary number of components is discussed, as well as the orbital stability of the corresponding standing waves for the related Schrödinger systems.
Minimax principle; Nonlinear Schrödinger systems; Normalized solutions; Orbital stability; Mathematics (all); Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1007043
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