Thumbnail - No thumbnail

Nonlinear Dirac Equation on Graphs with Localized Nonlinearities : Bound States and Nonrelativistic Limit

Borrelli, William; Carlone, Raffaele; Tentarelli, Lorenzo (2019), Nonlinear Dirac Equation on Graphs with Localized Nonlinearities : Bound States and Nonrelativistic Limit, SIAM Journal on Mathematical Analysis, 51, 2, p. 34. 10.1137/18M1211714

View/Open
Type
Article accepté pour publication ou publié
Date
2019
Journal name
SIAM Journal on Mathematical Analysis
Volume
51
Number
2
Publisher
SIAM - Society for Industrial and Applied Mathematics
Published in
Paris
Pages
34
Publication identifier
Metadata
Show full item record
Author(s)
Borrelli, William
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Carlone, Raffaele
Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”
Tentarelli, Lorenzo
Dipartimento di Matematica "Guido Castelnuovo" [Roma I] [Sapienza University of Rome]
Abstract (EN)
In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices. Precisely, we discuss existence and multiplicity of the bound states (arising as critical points of the NLD action functional) and we prove that, in the L 2-subcritical case, they converge to the bound states of the NLS equation in the nonrelativistic limit.
Subjects / Keywords
nonlinear Dirac equationsmetric graphs; nonrelativistic limit; variational methods; bound states; linking