| Issue |
Math. Model. Nat. Phenom.
Volume 11, Number 2, 2016
Spectral problems
|
|
|---|---|---|
| Page(s) | 20 - 35 | |
| DOI | https://doi.org/10.1051/mmnp/201611202 | |
| Published online | 21 March 2016 | |
Ground States for NLS on Graphs: a Subtle Interplay of Metric and Topology
Dipartimento di Scienze Matematiche “G.L. Lagrange”,
Politecnico di Torino C.so Duca
degli Abruzzi 24, 10129
Torino,
ITALY
⋆ Corresponding author. E-mail: adami.riccardo@gmail.com
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.
Mathematics Subject Classification: 35Q55 / 35P30
Key words: Nonlinear Schrödinger equation / graphs / ground states
© EDP Sciences, 2016
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