Ground States for NLS on Graphs: a Subtle Interplay of Metric and Topology

R. Adami¹

¹ Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino C.so Duca degli Abruzzi 24, 10129 Torino, ITALY

Mathematical modelling of natural phenomena, Tome 11 (2016) no. 2, pp. 20-35

Résumé

We review some recent results on the minimization of the energy associated to the nonlinear Schrödinger Equation on non-compact graphs. Starting from seminal results given by the author together with C. Cacciapuoti, D. Finco, and D. Noja for the star graphs, we illustrate the achiements attained for general graphs and the related methods, developed in collaboration with E. Serra and P. Tilli. We emphasize ideas and examples rather than computations or proofs.

Détail

DOI : 10.1051/mmnp/201611202

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