Multiple positive solutions for a Schrodinger-Poisson-Slater system

被引：60

作者：

Siciliano, Gaetano ^{[1
]}

机构：

[1] Univ Granada, Dpto Anal Matemat, E-18071 Granada, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 365卷 / 01期

关键词：

Schrodinger-Poisson system; Lusternik-Schnirelmann category; Multiplicity result; MAXWELL EQUATIONS; BOUND-STATES; SEMICLASSICAL STATES; ELLIPTIC PROBLEMS; DOMAIN TOPOLOGY; EXISTENCE; EXPONENT;

D O I：

10.1016/j.jmaa.2009.10.061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the existence of positive solutions to the following Schrodinger-Poisson-Slater system {-Delta u + u + lambda phi u = vertical bar u vertical bar(p-2)u in Omega, -Delta phi = u(2) in Omega, u = phi = 0 on partial derivative Omega, where Omega is a bounded domain in R-3, lambda is a fixed positive parameter nd p < 2* = 2N/N-2' We prove that if p is "near" the critical Sobolev exponent 2*, then the number of positive solutions is greater then the Lusternik-Schnirelmann category of Omega. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：288 / 299

页数：12

共 29 条

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

Ambrosetti, Antonio ;

Ruiz, David .

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

[2]

[Anonymous], 1996, VARIATIONAL METHODS, DOI DOI 10.1007/978-3-662-03212-1

[3]

[Anonymous], CAMBRIDGE STUD ADV M

[4] 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

[5] THE EFFECT OF THE DOMAIN TOPOLOGY ON THE NUMBER OF POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC PROBLEMS [J].

BENCI, V ;

CERAMI, G .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1991, 114 (01) :79-93

[6] 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

[7]

Benci V., 1998, TOPOL METHOD NONL AN, V11, P283

[8]

BENCI V, 1991, SC NORM SUPER PISA Q, P93

[9]

Bleecker D., 2005, GAUGE THEORY VARIATI

[10] On an exchange interaction model for quantum transport:: The Schrodinger-Poisson-Slater system [J].

Bokanowski, O ;

López, JL ;

Soler, J .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2003, 13 (10) :1397-1412

← 1 2 3 →