Multiple solutions for nonhomogeneous Schrodinger-Maxwell and Klein- Gordon-Maxwell equations on R 3

被引：35

作者：

Chen, Shang-Jie ^{[1
]}

Tang, Chun-Lei ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2010年 / 17卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Schrodinger-Maxwell equations; Klein-Gordon-Maxwell equations; Nonhomogeneous; Superlinear; Ekeland's variational principle; Mountain Pass Theorem; Variational methods; SOLITARY WAVES; POSITIVE SOLUTIONS; POISSON EQUATIONS; GROUND-STATE; EXISTENCE; SYSTEM; NONEXISTENCE; FIELD; R-3;

D O I：

10.1007/s00030-010-0068-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the following nonhomogeneous Schrodinger-Maxwell equations {-Delta u + V(x)u + phi u = f(x, u) + h(x), in R-3, -Delta phi = u(2), in R-3, where f satisfies the Ambrosetti-Rabinowitz type condition. Under appropriate assumptions on V, f and h, the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. Similar results for the nonhomogeneous Klein-Gordon-Maxwell equations {-Delta u + [m(2) - (omega + phi)(2)]u = vertical bar mu vertical bar(q-2)u + h(x), in R-3, {-Delta phi + phi mu(2) = -omega mu(2), in R-3, are also obtained when 2 < q < 6.

引用

页码：559 / 574

页数：16

共 50 条

[41] MULTIPLICITY OF SOLUTIONS FOR THE NONLINEAR SCHRODINGER-MAXWELL SYSTEM [J].

Fang, Yanqin ;

Zhang, Jihui .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2011, 10 (04) :1267-1279

[42] Infinitely many solutions for a nonlinear Klein-Gordon-Maxwell System [J].

Li, Lin ;

Tang, Chun-Lei .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 110 :157-169

[43] Solutions to the critical Klein-Gordon-Maxwell system with external potential [J].

Zhang, Jian .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 455 (02) :1152-1177

[44] Klein-Gordon-Maxwell Equations Driven by Mixed Local-Nonlocal Operators [J].

Cangiotti, Nicolo ;

Caponi, Maicol ;

Maione, Alberto ;

Vitillaro, Enzo .

MILAN JOURNAL OF MATHEMATICS, 2023, 91 (02) :375-403

[45] MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS SCHRODINGER-POISSON EQUATIONS WITH SIGN-CHANGING POTENTIAL [J].

Wang, Lixia ;

Ma, Shiwang ;

Xu, Na .

ACTA MATHEMATICA SCIENTIA, 2017, 37 (02) :555-572

[46] Hamiltonian formulation of the Klein-Gordon-Maxwell equations [J].

Benci, Vieri ;

Fortunato, Donato .

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2011, 22 (02) :113-134

[47] Multiple normalized solutions for Schrodinger-Maxwell equation with Sobolev critical exponent and mixed nonlinearities [J].

Kang, Jin-Cai ;

Li, Yong-Yong ;

Tang, Chun-Lei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2025, 443

[48] Improved results of nontrivial solutions for a nonlinear nonhomogeneous Klein-Gordon-Maxwell system involving sign-changing potential [J].

Gan, Canlin ;

Xiao, Ting ;

Zhang, Qiongfen .

ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)

[49] Multiple solutions for the nonhomogeneous Schrodinger-Poisson equations involving the fractional Laplacian [J].

Tong, Yanchun ;

Sun, Decai .

2018 17TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING AND APPLICATIONS FOR BUSINESS ENGINEERING AND SCIENCE (DCABES), 2018, :335-338

[50] Spinning Q-Balls for the Klein-Gordon-Maxwell Equations [J].

Benci, Vieri ;

Fortunato, Donato .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 295 (03) :639-668

← 1 2 3 4 5 →