Archivio Istituzionale della RicercaWe 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. - 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.
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Tentarelli L., NLS ground states on metric graphs with localized nonlinearities, 2016.pdf
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https://hdl.handle.net/11583/2662909