Ground states for the NLS equation with combined nonlinearities on non-compact metric graphs

We investigate the existence of ground states with prescribed mass for the NLS energy with combined $L^2$-critical and subcritical nonlinearities, on a general noncompact metric graph $mathcal G$. The interplay between the different nonlinearities creates new phenomena with respect to purely critical or subcritical problems on graphs; from a different perspective, topological and metric properties of the underlying graph drastically influence existence and nonexistence of ground states with respect to the analogue problem on the real line. Read More: https://epubs.siam.org/doi/abs/10.1137/20M1377837