Multi-bump solutions to a nonlinear Schrodinger equation with steep magnetic wells

被引：2

作者：

Shirai, Shin-ichi ^{[1
]}

机构：

[1] Osaka Inst Technol, Dept Math, Asahi Ku, Osaka 5358585, Japan

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2015年 / 56卷 / 09期

关键词：

POSITIVE SOLUTIONS; ELECTROMAGNETIC-FIELDS; ELLIPTIC PROBLEMS; CRITICAL GROWTH; R-N; MULTIPLICITY; EXISTENCE; ENERGY; R(N);

D O I：

10.1063/1.4930247

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show the existence of multi-bump solutions to a magnetic nonlinear Schrodinger equation with subcritical superlinear nonlinearity, -(del-i lambda A)(2)u = f (|u|(2)) u on R-N under some assumptions. Moreover, we show that the solutions are localized near every prescribed connected component of the interior of the zero set of the magnetic field B = dA as lambda ->infinity. (C) 2015 AIP Publishing LLC.

引用

页数：19

共 24 条

[1] Multiplicity of positive solutions for a class of problems with exponential critical growth in R2 [J].

Alves, Claudianor O. ;

Souto, Marco A. S. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (06) :1502-1520

[2]

Alves CO, 2009, TOPOL METHOD NONL AN, V34, P231

[3] MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF PROBLEMS WITH CRITICAL GROWTH IN RN [J].

Alves, Claudianor O. ;

de Morais Filho, Daniel C. ;

Souto, Marco A. S. .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2009, 52 :1-21

[4]

[Anonymous], 2010, FUNCTIONAL ANAL

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

Bartsch, T ;

Pankov, A ;

Wang, ZQ .

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

[6] Multiple positive solutions for a nonlinear Schrodinger equation [J].

Bartsch, T ;

Wang, ZQ .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2000, 51 (03) :366-384

[7] 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

[8] MULTIBUMP SOLUTIONS OF NONLINEAR SCHRODINGER EQUATIONS WITH STEEP POTENTIAL WELL AND INDEFINITE POTENTIAL [J].

Bartsch, Thomas ;

Tang, Zhongwei .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (01) :7-26

[9]

Cycon H.L., 1987, TEXTS MONOGRAPHS PHY

[10] Multiplicity of positive solutions of a nonlinear Schrodinger equation [J].

Ding, YH ;

Tanaka, K .

MANUSCRIPTA MATHEMATICA, 2003, 112 (01) :109-135

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