Calculus of Variations and Geometric Measure Theory

W. Borrelli - R. Carlone - L. Tentarelli

Nonlinear Dirac Equation On Graphs With Localized Nonlinearities: Bound States And Nonrelativistic Limit

created by borrelli on 19 Jul 2018
modified by tentarelli on 07 Jul 2022


Published Paper

Inserted: 19 jul 2018
Last Updated: 7 jul 2022

Journal: SIAM J. Math. Anal.
Volume: 51
Number: 2
Pages: 1046-1081
Year: 2019
Doi: 10.1137/18M1211714

ArXiv: 1807.06937 PDF


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.