We consider the Schrödinger equation with a subcritical focusing power nonlinearity on a noncompactmetricgraph,andprovethatforeveryfiniteedgethereexistsathresholdvalueof themass,beyondwhichthereexistsapositiveboundstateachievingitsmaximumonthatedge only. This bound state is characterized as a minimizer of the energy functional associated to the NLS equation, with an additional constraint (besides the mass prescription): this requires particular care in proving that the minimizer satisfies the Euler–Lagrange equation. As a consequence, for a sufficiently large mass every finite edge of the graph hosts at least one positive bound state that, owing to its minimality property, is orbitally stable.

Multiple positive bound states for the subcritical NLS equation on metric graphs / Adami, Riccardo; Serra, Enrico; Tilli, Paolo. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 58:1(2019). [10.1007/s00526-018-1461-4]

### Multiple positive bound states for the subcritical NLS equation on metric graphs

#### Abstract

We consider the Schrödinger equation with a subcritical focusing power nonlinearity on a noncompactmetricgraph,andprovethatforeveryfiniteedgethereexistsathresholdvalueof themass,beyondwhichthereexistsapositiveboundstateachievingitsmaximumonthatedge only. This bound state is characterized as a minimizer of the energy functional associated to the NLS equation, with an additional constraint (besides the mass prescription): this requires particular care in proving that the minimizer satisfies the Euler–Lagrange equation. As a consequence, for a sufficiently large mass every finite edge of the graph hosts at least one positive bound state that, owing to its minimality property, is orbitally stable.
##### Scheda breve Scheda completa Scheda completa (DC)
File in questo prodotto:
File
AST_multiple_bound_states.pdf

non disponibili

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 681.32 kB
Formato Adobe PDF
adami_serra_tilli_multiple_positive_bound_states.pdf

non disponibili

Tipologia: 1. Preprint / submitted version [pre- review]
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 210.23 kB
Formato Adobe PDF
##### Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

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/11583/2729938`