MULTIPLICITY OF SOLUTIONS FOR THE NONLINEAR SCHRODINGER-MAXWELL SYSTEM

被引：5

作者：

Fang, Yanqin ^{[1
]}

Zhang, Jihui ^{[1
]}

机构：

[1] Nanjing Normal Univ, Jiangsu Key Lab NSLSCS, Sch Math Sci, Nanjing 210046, Jiangsu, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2011年 / 10卷 / 04期

关键词：

Schrodinger-Maxwell; Ljusternik-Schnirelmann theory; multiple solutions; POSITIVE SOLUTIONS; POISSON PROBLEM; SEMICLASSICAL STATES; BOUND-STATES; EQUATIONS; POTENTIALS; MOLECULES; SPHERES; WAVES; ATOMS;

D O I：

10.3934/cpaa.2011.10.1267

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 system -epsilon(2)Delta v + V(x)v + psi(x)v = v(p), x is an element of R(3), -Delta psi = 1/epsilon v(2), lim(vertical bar x vertical bar -> infinity)psi(x) = 0, x is an element of R(3), where epsilon > 0, p is an element of (3, 5), V is positive potential. We relate the number of solutions with topology of the set where V attain their minimum value. By applying Ljusternik-Schnirelmann theory, we prove the multiplicity of solutions.

引用

页码：1267 / 1279

页数：13

共 24 条

[1]

Alves C.O., 2005, NODEA-NONLINEAR DIFF, V12, P437

[2] MULTIPLICITY OF SOLUTIONS FOR ELLIPTIC SYSTEMS VIA LOCAL MOUNTAIN PASS METHOD [J].

Alves, Claudianor O. ;

Figueiredo, Giovany M. ;

Furtado, Marcelo F. .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (06) :1745-1758

[3] On multiplicity and concentration of positive solutions for a class of quasilinear problems with critical exponential growth in RN [J].

Alves, Claudianor O. ;

Figueiredo, Giovany M. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (03) :1288-1311

[4] Multiplicity results for some nonlinear Schrodinger equations with potentials [J].

Ambrosetti, A ;

Malchiodi, A ;

Secchi, S .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 159 (03) :253-271

[5]

[Anonymous], 1997, Topol. Methods Nonlinear Anal, DOI DOI 10.12775/TMNA.1997.019

[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]

AZZOLLINI A, 2009, B UNIONE MAT ITAL, V9, P93

[8] MULTIPLE POSITIVE SOLUTIONS OF SOME ELLIPTIC PROBLEMS VIA THE MORSE-THEORY AND THE DOMAIN TOPOLOGY [J].

BENCI, V ;

CERAMI, G .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1994, 2 (01) :29-48

[9] THE THOMAS-FERMI-VONWEIZSACKER THEORY OF ATOMS AND MOLECULES [J].

BENGURIA, R ;

BREZIS, H ;

LIEB, EH .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1981, 79 (02) :167-180

[10] Standing waves for nonlinear Schrodinger equations with singular potentials [J].

Byeon, Jaeyoung ;

Wang, Zhi-Qiang .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (03) :943-958

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