Infinitely many solutions for Schrodinger-Maxwell equations with indefinite sign subquadratic potentials

被引：28

作者：

Chen, Peng ^{[1
]}

Tian, Cai ^{[2
]}

机构：

[1] China Three Gorges Univ, Coll Sci, Yichang 443002, Hubei, Peoples R China

[2] Wuhan Univ Technol, Sch Transportat, Wuhan 430070, Hubei, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 226卷

关键词：

Schrodinger-Maxwell equations; Sublinear; Genus; Critical point theory; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; POISSON SYSTEMS; SOLITARY WAVES; BOUND-STATES; EXISTENCE;

D O I：

10.1016/j.amc.2013.10.069

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with multiplicity of solutions of a class of sublinear Schrodinger-Maxwell equations {-Delta u + V(x)u + phi u = f (x, u), in R-3, -Delta phi = u(2); lim(vertical bar x vertical bar ->infinity) phi(x) = 0, in R-3. Under more relaxed assumptions on V and f, we establish some existence criteria to guarantee that the above problem has at least one or infinitely many nontrivial solutions by using the genus properties in critical theory. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：492 / 502

页数：11

共 34 条

[1] A nonlinear superposition principle and multibump solutions of periodic Schrodinger equations [J].

Ackermann, N .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 234 (02) :277-320

[2] Multiple bound states for the Schrodinger-Poisson problem [J].

Ambrosetti, Antonio ;

Ruiz, David .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2008, 10 (03) :391-404

[3] On Schrodinger-Poisson Systems [J].

Ambrosetti, Antonio .

MILAN JOURNAL OF MATHEMATICS, 2008, 76 (01) :257-274

[4]

[Anonymous], 1989, APPL MATH SCI

[5]

[Anonymous], 1986, CBMS REG C SER MATH

[6] Ground state solutions for the nonlinear Schrodinger-Maxwell equations [J].

Azzollini, A. ;

Pomponio, A. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 345 (01) :90-108

[7] INFINITELY MANY RADIAL SOLUTIONS OF A SEMILINEAR ELLIPTIC PROBLEM ON R(N) [J].

BARTSCH, T ;

WILLEM, M .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1993, 124 (03) :261-276

[8] Nonlinear Schrodinger equations with steep potential well [J].

Bartsch, T ;

Pankov, A ;

Wang, ZQ .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2001, 3 (04) :549-569

[9] EXISTENCE AND MULTIPLICITY RESULTS FOR SOME SUPERLINEAR ELLIPTIC PROBLEMS ON R(N) [J].

BARTSCH, T ;

WANG, ZQ .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (9-10) :1725-1741

[10] Solitons and the electromagnetic field [J].

Benci, V ;

Fortunato, D ;

Masiello, A ;

Pisani, L .

MATHEMATISCHE ZEITSCHRIFT, 1999, 232 (01) :73-102

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