Abstract
We review some recent results on the existence of the ground state for a nonlinear Schrodinger equation (NLS) posed on a graph or network composed of a generic compact part to which a finite number of half-lines are attached. In particular we concentrate on the main theorem in Cacciapuoti et al. (Ground state and orbital stability for the NLS equation on a general starlike graph with potentials, preprint arXiv:1608.01506) which covers the most general setting and we compare it with similar results.
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