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

Adami, Riccardo;Serra, Enrico;Tilli, Paolo
2019

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2729938