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Non-Kirchhoff Vertices and Nonlinear Schrödinger Ground States on Graphs

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Dipartimento di Scienze Matematiche “G.L. Lagrange”, Politecnico di Torino Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
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Dipartimento di Matematica “G. Peano”, Università di Torino Via Carlo Alberto 10, 10123 Torino, Italy
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 617; https://doi.org/10.3390/math8040617
Received: 12 March 2020 / Revised: 9 April 2020 / Accepted: 9 April 2020 / Published: 17 April 2020
(This article belongs to the Special Issue Mathematical Methods in Nonlinear Waves and Dynamical Systems)
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. View Full-Text
Keywords: quantum graphs; Nonlinear Schrödinger Equation; ground states quantum graphs; Nonlinear Schrödinger Equation; ground states
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Adami, R.; Boni, F.; Ruighi, A. Non-Kirchhoff Vertices and Nonlinear Schrödinger Ground States on Graphs. Mathematics 2020, 8, 617.

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