The paper deals with the existence of normalized solutions to the system −Δu−λ1u=μ1u3+βuv2in R3−Δv−λ2v=μ2v3+βu2vin R3∫R3u2=a12and∫R3v2=a22 for any μ1,μ2,a1,a2>0 and β<0 prescribed. We present a new approach that is based on the introduction of a natural constraint associated to the problem. We also show that, as β→−∞, phase separation occurs for the solutions that we find. Our method can be adapted to scalar nonlinear Schrödinger equations with normalization constraint, and leads to alternative and simplified proofs to some results already available in the literature.

A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems

Soave, Nicola
2017

Abstract

The paper deals with the existence of normalized solutions to the system −Δu−λ1u=μ1u3+βuv2in R3−Δv−λ2v=μ2v3+βu2vin R3∫R3u2=a12and∫R3v2=a22 for any μ1,μ2,a1,a2>0 and β<0 prescribed. We present a new approach that is based on the introduction of a natural constraint associated to the problem. We also show that, as β→−∞, phase separation occurs for the solutions that we find. Our method can be adapted to scalar nonlinear Schrödinger equations with normalization constraint, and leads to alternative and simplified proofs to some results already available in the literature.
Elliptic systems; Min–max methods; Natural constraint; Schrödinger systems; Analysis
File in questo prodotto:
File Dimensione Formato  
11311-1036167_Soave.pdf

accesso aperto

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 623.18 kB
Formato Adobe PDF
623.18 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1036167
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 69
  • ???jsp.display-item.citation.isi??? 62
social impact