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.