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
[21]   Multiple positive solutions for degenerate elliptic equations with singularity and critical cone Sobolev exponents [J].
Haining Fan .
Journal of Pseudo-Differential Operators and Applications, 2019, 10 :689-709
[22]   Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent [J].
Daisuke Naimen .
Nonlinear Differential Equations and Applications NoDEA, 2014, 21 :885-914
[23]   Positive solutions of Kirchhoff type elliptic equations involving a critical Sobolev exponent [J].
Naimen, Daisuke .
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2014, 21 (06) :885-914
[24]   SOLUTIONS FOR THE QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS [J].
Kang Dongsheng .
ACTA MATHEMATICA SCIENTIA, 2010, 30 (05) :1529-1540
[25]   Multiplicity of positive solutions for a class of critical Sobolev exponent problems involving Kirchhoff-type nonlocal term [J].
Duan, Yu ;
Sun, Xin ;
Liao, Jia-Feng .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (12) :4427-4437
[26]   SOLUTIONS FOR THE QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS [J].
康东升 .
ActaMathematicaScientia, 2010, 30 (05) :1529-1540
[27]   ON NEUMANN PROBLEM FOR SOMESEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].
谢资清 .
ActaMathematicaScientia, 1998, (02) :186-196
[28]   EXISTENCE RESULTS FOR DEGENERATE ELLIPTIC EQUATIONS WITH CRITICAL CONE SOBOLEV EXPONENTS [J].
范海宁 ;
刘晓春 .
Acta Mathematica Scientia, 2014, 34 (06) :1907-1921
[29]   MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH [J].
Liao, Jianfeng ;
Pu, Yang ;
Tang, Chunlei .
ACTA MATHEMATICA SCIENTIA, 2018, 38 (02) :497-518
[30]   MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH [J].
廖家锋 ;
蒲洋 ;
唐春雷 .
Acta Mathematica Scientia, 2018, (02) :497-518
12345