Multiplicity of positive solutions for a nonlinear Schrodinger-Poisson system

被引：80

作者：

Sun, Juntao ^{[1
]}

Wu, Tsung-fang ^{[2
]}

Feng, Zhaosheng ^{[3
]}

机构：

[1] Shandong Univ Technol, Sch Sci, Zibo 255049, Peoples R China

[2] Natl Univ Kaohsiung, Dept Appl Math, Kaohsiung 811, Taiwan

[3] Univ Texas Rio Grande Valley, Dept Math, Edinburg, TX 78539 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 01期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Positive solutions; Sobolev embedding theorem; Schrodinger Poisson system; Radial solution; Barycenter map; Concentration-compactness principle; CONCENTRATION-COMPACTNESS PRINCIPLE; GROUND-STATE SOLUTIONS; NODAL SOLUTIONS; EXISTENCE; EQUATION; CALCULUS;

D O I：

10.1016/j.jde.2015.09.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the multiplicity of positive solutions for a nonlinear Schrodinger Poisson system: {-Delta U + lambda U + K (x) phi u = Q(x) broken vertical bar u broken vertical bar(p-2) u in R-3,R- -Delta phi = K(x) u(2) in R-3, where lambda > 0, 2 < p < 6, and both K(x) and Q(x) are nonnegative and uniformly continuous functions on R-3. We show that the number of positive solutions is dependent on the profile of Q (x). Some novel results are presented which improve and generalize the existing ones in the literature. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：586 / 627

页数：42

共 35 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], 1997, Minimax theorems

[3]

Aprile T., 2004, ADV NONLINEAR STUD, V4, P307

[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] Concentration and compactness in nonlinear Schrodinger-Poisson system with a general nonlinearity [J].

Azzollini, A. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (07) :1746-1763

[6] Three nodal solutions of singularly perturbed elliptic equations on domains without topology [J].

Bartsch, T ;

Weth, T .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2005, 22 (03) :259-281

[7]

Benci V., 1998, Topol. Methods Nonlinear Anal., V11, P283

[8]

Binding P. A., 1997, ELECT J DIFFERENTIAL, V1997, P1

[9] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS [J].

BREZIS, H ;

LIEB, E .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) :486-490

[10]

Brown KJ, 2009, DIFFER INTEGRAL EQU, V22, P1097

← 1 2 3 4 →