Schrodinger-Maxwell systems on non-compact Riemannian manifolds

被引：11

作者：

Farkas, Csaba ^{[1
]}

Kristaly, Alexandru ^{[2
,3
]}

机构：

[1] Sapientia Univ, Dept Math & Informat, Targu Mures, Romania

[2] Univ Babes Bolyai, Dept Econ, R-3400 Cluj Napoca, Romania

[3] Obuda Univ, Inst Appl Math, H-1034 Budapest, Hungary

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2016年 / 31卷

关键词：

Schrodinger-Maxwell system; Riemannian manifold; Non-compact; Isometry; Existence; Multiplicity; KLEIN-GORDON-MAXWELL; SYMMETRIC CRITICALITY; FINSLER GEOMETRY; EQUATIONS; PRINCIPLE;

D O I：

10.1016/j.nonrwa.2016.03.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study nonlinear Schrodinger-Maxwell systems on n-dimensional non-compact Riemannian manifolds of Hadamard type, 3 <= n <= 5. The main difficulty resides in the lack of compactness which is recovered by exploring suitable isometric actions of the Hadamard manifolds. By combining variational arguments, some existence, uniqueness and multiplicity of isometry-invariant weak solutions are established for the Schrodinger-Maxwell system depending on the behavior of the nonlinear term. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：473 / 491

页数：19

共 35 条

[1] Multiple bound states for the Schrodinger-Poisson problem
Ambrosetti, Antonio
Ruiz, David
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2008, 10 (03) : 391 - 404
[2] [Anonymous], 2010, FUNCTIONAL ANAL
[3] Concentration and compactness in nonlinear Schrodinger-Poisson system with a general nonlinearity
Azzollini, A.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (07) : 1746 - 1763
[4] On the Schrodinger-Maxwell equations under the effect of a general nonlinear term
Azzollini, A.
d'Avenia, P.
Pomponio, A.
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (02): : 779 - 791
[5] Benci V., 1998, Topol. Methods Nonlinear Anal., V11, P283
[6] Bridson M. R., 1999, GRUND MATH WISS, V319, DOI DOI 10.1007/978-3-662-12494-9
[7] Positive solutions for some non-autonomous Schrodinger-Poisson systems
Cerami, Giovanna
Vaira, Giusi
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (03) : 521 - 543
[8] Solitary waves for nonlinear Klein-Gordon-Maxwell and Schrodinger-Maxwell equations
D'Aprile, T
Mugnai, D
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2004, 134 : 893 - 906
[9] Non-existence results for the coupled Klein-Gordon-Maxwell equations
D'Aprile, T
Mugnai, D
[J]. ADVANCED NONLINEAR STUDIES, 2004, 4 (03) : 307 - 322
[10] d'Avenia P, 2002, ADV NONLINEAR STUD, V2, P177

← 1 2 3 4 →