Existence and multiplicity of positive solutions for a class of elliptic equations involving critical Sobolev exponents

被引：0
作者：
Jia-feng Liao
Jiu Liu
Peng Zhang
Chun-Lei Tang
机构：
[1] Southwest University,School of Mathematics and Statistics
[2] Zunyi Normal College,School of Mathematics and Computational Science
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2016年 / 110卷
关键词：
Elliptic equations; Critical exponent; Positive solution; Variational method; Nehari method; 35B09; 35B33; 35J20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider a class of elliptic equations involving critical Sobolev exponents. By the variational method and the Nehari method, we obtain the existence and multiplicity of positive solutions. We point out that the relation between the number of the maxima of the coefficient function of the critical term and the number of the positive solutions for the problem.
引用
收藏
页码：483 / 501
页数：18
相关论文
共 50 条
[41]   Solutions for a class of quasilinear Schrodinger equations with critical Sobolev exponents [J].
Li, Zhouxin ;
Zhang, Yimin .
JOURNAL OF MATHEMATICAL PHYSICS, 2017, 58 (02)
[42]   On Neumann problem for some semilinear elliptic equations involving critical Sobolev exponents [J].
Xie, ZQ .
ACTA MATHEMATICA SCIENTIA, 1998, 18 (02) :186-196
[43]   On the singular elliptic systems involving multiple critical Sobolev exponents [J].
Huang, Yan ;
Kang, Dongsheng .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (02) :400-412
[44]   Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev exponent [J].
Liao, Jia-Feng ;
Li, Hong-Ying ;
Zhang, Peng .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (03) :787-797
[45]   Existence and multiplicity of positive solutions for some Hardy-Sobolev critical elliptic equation with boundary singularities [J].
Shang, Yan-Ying .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (05) :2724-2734
[46]   Existence of a ground state solution for Choquard equations involving critical Sobolev exponents [J].
Li, Gui-Dong ;
Tang, Chun-Lei .
ANNALES POLONICI MATHEMATICI, 2019, 122 (02) :165-179
[47]   Existence and multiplicity of positive solutions to quasilinear elliptic equations with two parameters [J].
Jeong J. ;
Kim C.-G. .
Afrika Matematika, 2017, 28 (1-2) :237-247
[48]   Existence and multiplicity of positive solutions of semilinear elliptic equations in unbounded domains [J].
Hu, Kai ;
Tang, Chun-Lei .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (03) :609-629
[49]   Multiple positive solutions for an elliptic problem involving a critical Sobolev exponent [J].
Zheng, Tiantian ;
Wang, Zhiyong ;
Ma, Pei ;
Zhang, Jihui .
APPLICABLE ANALYSIS, 2022, 101 (15) :5334-5357
[50]   Existence result for semilinear elliptic systems involving critical exponents [J].
S Khademloo ;
M Farzinejad ;
O Khazaee kohpar .
Boundary Value Problems, 2012
12345