NLS ground states on metric graphs with localized nonlinearities

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.

18 pages

References in corpus (1)

• The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit

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