ON SEMILOCAL KLEIN-GORDON-MAXWELL EQUATIONS

被引：1

作者：

Han, Jongmin ^{[1
]}

Sohn, Juhee ^{[2
]}

Yo, Yeong Seok ^{[1
]}

机构：

[1] Kyung Hee Univ, Dept Math, Seoul 02447, South Korea

[2] Kookmin Univ, Coll Gen Educ, Seoul 02707, South Korea

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2021年 / 58卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

Semilocal gauge field model; Klein-Gordon-Maxwell equations; mountain pass solutions; Pohozaev identity; SOLITARY WAVES; EXISTENCE; NONEXISTENCE; STRINGS; SYSTEM;

D O I：

10.4134/JKMS.j200463

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the Klein-Gordon-Maxwell equations arising from a semilocal gauge field model. This model describes the interaction of two complex scalar fields and one gauge field, and generalizes the classical Klein-Gordon equation coupled with the Maxwell electrodynamics. We prove that there exist infinitely many standing wave solutions for p is an element of (2, 6) which are radially symmetric. Here, p comes from the exponent of the potential of scalar fields. We also prove the nonexistence of nontrivial solutions for the critical case p = 6.

引用

页码：1131 / 1145

页数：15

共 18 条

[1]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[2] Improved estimates and a limit case for the electrostatic Klein-Gordon-Maxwell system [J].

Azzollini, A. ;

Pisani, L. ;

Pomponio, A. .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2011, 141 :449-463

[3]

Azzollini A, 2010, TOPOL METHOD NONL AN, V35, P33

[4] Solitary waves of the nonlinear Klein-Gordon equation coupled with the Maxwell equations [J].

Benci, V ;

Fortunato, D .

REVIEWS IN MATHEMATICAL PHYSICS, 2002, 14 (04) :409-420

[5] Positive ground state solutions for the critical Klein-Gordon-Maxwell system with potentials [J].

Carriao, Paulo C. ;

Cunha, Patricia L. ;

Miyagaki, Olimpio H. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (10) :4068-4078

[6] EXISTENCE RESULTS FOR THE KLEIN-GORDON-MAXWELL EQUATIONS IN HIGHER DIMENSIONS WITH CRITICAL EXPONENTS [J].

Carriao, Paulo C. ;

Cunha, Patricia L. ;

Miyagaki, Olimpio H. .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2011, 10 (02) :709-718

[7] Existence and non-existence of solitary waves for the critical Klein-Gordon equation coupled with of Maxwell's equations [J].

Cassani, D .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 58 (7-8) :733-747

[8] EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR KLEIN-GORDON-MAXWELL SYSTEM WITH A PARAMETER [J].

Che, Guofeng ;

Chen, Haibo .

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (03) :1015-1030

[9] Multiple solutions for nonhomogeneous Klein-Gordon-Maxwell equations on R3 [J].

Chen, Shang-Jie ;

Song, Shu-Zhi .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 22 :259-271

[10] IMPROVED RESULTS FOR KLEIN-GORDON-MAXWELL SYSTEMS WITH GENERAL NONLINEARITY [J].

Chen, Sitong ;

Tang, Xianhua .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018, 38 (05) :2333-2348

← 1 2 →