NONLINEAR DIRAC EQUATION ON GRAPHS WITH LOCALIZED NONLINEARITIES: BOUND STATES AND NONRELATIVISTIC LIMIT

被引：25

作者：

Borrelli, William ^{[1
]}

Carlone, Raffaele ^{[2
]}

Tentarelli, Lorenzo ^{[2
]}

机构：

[1] Univ Paris 09, PSL Res Univ, CNRS, UMR 7534, F-75016 Paris, France

[2] Univ Federico II Napoli, Dipartimento Matemat & Applicaz R Caccioppoli, MSA, Via Cinthia, I-80126 Naples, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2019年 / 51卷 / 02期

关键词：

nonlinear Dirac equations; metric graphs; nonrelativistic limit; variational methods; bound states; linking; GROUND-STATES; NLS EQUATION; SCHRODINGER-EQUATION; STATIONARY SOLUTIONS; STANDING WAVES; QUANTUM GRAPHS; METRIC GRAPHS; STABILITY; COMPACT; OPERATOR;

D O I：

10.1137/18M1211714

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 nonlinear Schrodinger equation in the nonrelativistic limit.

引用

页码：1046 / 1081

页数：36

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