Riccardo Adami, Enrico Serra, Paolo Tilli
Multiple positive bound states for the subcritical NLS equation on metric graphs
(58K, LaTex2)
ABSTRACT. We consider the Schroedinger equation with a subcritical focusing power
nonlinearity on a noncompact metric graph, and prove that for every finite edge
there exists a threshold value of the mass, beyond which there exists a positive
bound state achieving its maximum on that edge only. This bound
state is characterized as a minimizer of the energy functional
associated to the NLS equation, with an additional constraint (besides
the mass prescription): this requires particular care in proving that
the minimizer satisfies the Euler-Lagrange equation. As a
consequence, for a sufficiently large mass every finite edge of the
graph hosts at least one positive bound state that, owing to its
minimality property, is orbitally stable.