We investigate the existence of ground states for the focusing subcritical NLS energy on metric graphs with localized nonlinearities. In particular, we find two thresholds on the measure of the region where the nonlinearity is localized that imply, respectively, existence or nonexistence of ground states. In order to obtain these results we adapt to the context of metric graphs some classical techniques from the Calculus of Variations.

NLS ground states on metric graphs with localized nonlinearities / Tentarelli, Lorenzo. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 433:1(2016), pp. 291-304. [10.1016/j.jmaa.2015.07.065]

NLS ground states on metric graphs with localized nonlinearities

Tentarelli, Lorenzo
2016

Abstract

We investigate the existence of ground states for the focusing subcritical NLS energy on metric graphs with localized nonlinearities. In particular, we find two thresholds on the measure of the region where the nonlinearity is localized that imply, respectively, existence or nonexistence of ground states. In order to obtain these results we adapt to the context of metric graphs some classical techniques from the Calculus of Variations.
2016
Localized nonlinearity; Metric graphs; Minimization; NLS energy; Nonlinear Schrödinger equation; Analysis; Applied Mathematics
01 Pubblicazione su rivista::01a Articolo in rivista
NLS ground states on metric graphs with localized nonlinearities / Tentarelli, Lorenzo. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 433:1(2016), pp. 291-304. [10.1016/j.jmaa.2015.07.065]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1118904
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