ISOLATED SINGULARITY FOR SEMILINEAR ELLIPTIC EQUATIONS

被引：10
|
作者：
Wei, Lei [1 ]
Feng, Zhaosheng [2 ]
机构：
[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China
[2] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78539 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 07期
关键词：
Hardy potential; eigenvalue; super-subsolution method; minimal positive solution; BLOW-UP SOLUTIONS;
D O I：
10.3934/dcds.2015.35.3239
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a class of semilinear elliptic equations with the Hardy potential. By means of the super-subsolution method and the comparison principle, we explore the existence of a minimal positive solution and a maximal positive solution. Through a scaling technique, we obtain the asymptotic property of positive solutions near the origin. Finally, the nonexistence of a positive solution is proven when the parameter is larger than a critical value.
引用
收藏
页码：3239 / 3252
页数：14
相关论文
共 50 条
  • [21] Symmetry of the solutions of semilinear elliptic equations
    Dolbeault, J
    Felmer, P
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 329 (08): : 677 - 682
  • [22] On a class of semilinear elliptic equations in Rn
    Bae, S
    Chang, TK
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 185 (01) : 225 - 250
  • [23] TOPOLOGICAL DERIVATIVES FOR SEMILINEAR ELLIPTIC EQUATIONS
    Iguernane, Mohamed
    Nazarov, Serguei A.
    Roche, Jean-Rodolphe
    Sokolowski, Jan
    Szulc, Katarzyna
    INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE, 2009, 19 (02) : 191 - 205
  • [24] Uniqueness of continuation for semilinear elliptic equations
    Choulli, Mourad
    PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 5 (04):
  • [25] SEMILINEAR ELLIPTIC EQUATIONS WITH DEPENDENCE ON THE GRADIENT
    Liu, Guanggang
    Shi, Shaoyun
    Wei, Yucheng
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
  • [26] SEMILINEAR ELLIPTIC EQUATIONS ON FRACTAL SETS
    Chen Hua
    He Zhenya
    ACTA MATHEMATICA SCIENTIA, 2009, 29 (02) : 232 - 242
  • [27] On semilinear elliptic equations with diffuse measures
    Klimsiak, Tomasz
    Rozkosz, Andrzej
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2018, 25 (04):
  • [28] Solutions of Semilinear Elliptic Equations in Tubes
    Frank Pacard
    Filomena Pacella
    Berardino Sciunzi
    Journal of Geometric Analysis, 2014, 24 : 445 - 471
  • [29] Semilinear elliptic equations with singular nonlinearities
    Boccardo, Lucio
    Orsina, Luigi
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 37 (3-4) : 363 - 380
  • [30] Semilinear elliptic equations on rough domains
    Arendt, Wolfgang
    Daners, Daniel
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 346 : 376 - 415
12345