Riccardo Adami, Enrico Serra, Paolo Tilli
Threshold phenomena and existence results for NLS ground states on graphs
(68K, Latex2e)
ABSTRACT. We investigate the existence of ground states of prescribed mass, for the nonlinear Schroedinger energy on a noncompact metric graph G.
While in some cases the topology of G may rule out or, on the contrary,
guarantee the existence of ground states of any given mass, in general
also some metric properties of G, and their quantitative relation
with the actual value of the prescribed mass, are relevant as concerns the
existence of ground states.
This may give rise to interesting phase transitions from nonexistence to existence of ground states, when a certain quantity reaches a critical threshold.