We investigate the existence of ground states for the subcritical NLS energy on metric graphs. In particular, we find out a topological assumption that guarantees the nonexistence of ground states, and give an example in which the assumption is not fulfilled and ground states actually exist. In order to obtain the result, we introduce a new rearrangement technique, adapted to the graph where it applies. Owing to such a technique, the energy level of the rearranged function is improved by conveniently mixing the symmetric and monotone rearrangement procedures.

NLS ground states on graphs / Adami, Riccardo; Serra, Enrico; Tilli, Paolo. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 54:1(2015), pp. 743-761. [10.1007/s00526-014-0804-z]

NLS ground states on graphs

ADAMI, RICCARDO;SERRA, Enrico;TILLI, PAOLO
2015

Abstract

We investigate the existence of ground states for the subcritical NLS energy on metric graphs. In particular, we find out a topological assumption that guarantees the nonexistence of ground states, and give an example in which the assumption is not fulfilled and ground states actually exist. In order to obtain the result, we introduce a new rearrangement technique, adapted to the graph where it applies. Owing to such a technique, the energy level of the rearranged function is improved by conveniently mixing the symmetric and monotone rearrangement procedures.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2603580