We consider the nonlinear Schroedinger equation with focusing power-type nonlinearity on compact graphs with at least one terminal edge, i.e., an edge ending with a vertex of degree 1. On the one hand, we introduce the associated action functional, and we provide a profile description of positive low action solutions at large frequencies, showing that they concentrate on one terminal edge, where they coincide with suitable rescaling of the unique solution to the corresponding problem on the half-line. On the other hand, a Lyapunov-Schmidt reduction procedure is performed to construct one-peaked and multipeaked positive solutions with sufficiently large frequency, exploiting the presence of one or more terminal edges.

Peaked and low action solutions of NLS equations on graphs with terminal edges

Ghimenti M.;Micheletti A. M.;
2020-01-01

Abstract

We consider the nonlinear Schroedinger equation with focusing power-type nonlinearity on compact graphs with at least one terminal edge, i.e., an edge ending with a vertex of degree 1. On the one hand, we introduce the associated action functional, and we provide a profile description of positive low action solutions at large frequencies, showing that they concentrate on one terminal edge, where they coincide with suitable rescaling of the unique solution to the corresponding problem on the half-line. On the other hand, a Lyapunov-Schmidt reduction procedure is performed to construct one-peaked and multipeaked positive solutions with sufficiently large frequency, exploiting the presence of one or more terminal edges.
2020
Dovetta, S.; Ghimenti, M.; Micheletti, A. M.; Pistoia, A.
File in questo prodotto:
File Dimensione Formato  
Siam.pdf

non disponibili

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - accesso privato/ristretto
Dimensione 424.86 kB
Formato Adobe PDF
424.86 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
versione_arxiv.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 521.85 kB
Formato Adobe PDF
521.85 kB Adobe PDF Visualizza/Apri
SIAMoff.pdf

accesso aperto

Descrizione: offprint
Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 601.07 kB
Formato Adobe PDF
601.07 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: https://hdl.handle.net/11568/1056841
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 13
social impact