Riccardo Adami, Enrico Serra, Paolo Tilli
NLS ground states on graphs
(74K, Latex2e)
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.