Existence and multiplicity of solutions for critical elliptic equations with multi-polar potentials in symmetric domains

被引：4

作者：

Guo, Qianqiao ^{[1
]}

Han, Junqiang ^{[1
]}

Niu, Pengcheng ^{[1
]}

机构：

[1] Northwestern Polytech Univ, Dept Appl Math, Xian 710129, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 15期

基金：

中国国家自然科学基金;

关键词：

Elliptic equation; Sobolev exponent; Multi-polar potentials; Bounded symmetric domain; Positive solution; NONLINEAR SCHRODINGER-EQUATIONS; INVERSE-SQUARE POTENTIALS; CRITICAL SOBOLEV EXPONENT; POSITIVE SOLUTIONS;

D O I：

10.1016/j.na.2012.05.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the elliptic equations with critical Sobolev exponents and multi-polar potentials in bounded symmetric domains and prove the existence and multiplicity of symmetric positive solutions by using the Ekeland variational principle and the Lusternik-Schnirelmann category theory. (c) 2012 Elsevier Ltd. All rights reserved.

引用

页码：5765 / 5786

页数：22

共 36 条

[1]

Abdellaoui B, 2004, ADV DIFFERENTIAL EQU, V9, P481

[2]

Ambrosetti A, 1992, MEMOIRES SOC MATH FR, V49, P1, DOI [10.24003/msmf.362, DOI 10.24033/MSMF.362]

[3]

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

[4]

[Anonymous], 1996, ADV DIFFER EQU-NY

[5]

Aubin T., 1976, J. Diff. Geom., V11, P573

[6]

Badiale M, 2006, REND LINCEI-MAT APPL, V17, P1

[7] EXISTENCE OF POSITIVE SOLUTIONS OF THE EQUATION -DELTA-U+A(X)U=U(N+2)/(N-2) IN RN [J].

BENCI, V ;

CERAMI, G .

JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 88 (01) :90-117

[8] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

BREZIS, H ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) :437-477

[9] Solutions to critical elliptic equations with multi-singular inverse square potentials [J].

Cao, DM ;

Han, PG .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 224 (02) :332-372

[10] Solutions for semilinear elliptic equations with critical exponents and Hardy potential [J].

Cao, DM ;

Han, PG .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 205 (02) :521-537

← 1 2 3 4 →