Non-Kirchhoff Vertices and Nonlinear Schrödinger Ground States on Graphs

Riccardo Adami, Filippo Boni and Alice Ruighi
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Riccardo Adami: Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Filippo Boni: Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Alice Ruighi: Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

Mathematics, 2020, vol. 8, issue 4, 1-14

Abstract: We review some recent results and announce some new ones on the problem of the existence of ground states for the Nonlinear Schrödinger Equation on graphs endowed with vertices where the matching condition, instead of being free (or Kirchhoff’s), is non-trivially interacting. This category includes Dirac’s delta conditions, delta prime, Fülöp-Tsutsui, and others.

Keywords: quantum graphs; Nonlinear Schrödinger Equation; ground states (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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