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

被引：24
|
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
收藏
页码：1046 / 1081
页数：36
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