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

页码：3239 / 3252

页数：14

共 50 条

[1] Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity
Cirstea, Florica Corina
Du, Yihong
JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 250 (02) : 317 - 346
[2] Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity
Ghergu, Marius
Kim, Sunghan
Shahgholian, Henrik
ADVANCES IN NONLINEAR ANALYSIS, 2019, 8 (01) : 995 - 1003
[3] EXISTENCE OF SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS WITH VARIABLE EXPONENT SINGULARITY
Pandey, Ambesh Kumar
Kar, Rasmita
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2023, 53 (03) : 903 - 913
[4] Isolated boundary singularities of semilinear elliptic equations
Marie-Françoise Bidaut-Véron
Augusto C. Ponce
Laurent Véron
Calculus of Variations and Partial Differential Equations, 2011, 40 : 183 - 221
[5] Isolated boundary singularities of semilinear elliptic equations
Bidaut-Veron, Marie-Francoise
Ponce, Augusto C.
Veron, Laurent
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2011, 40 (1-2) : 183 - 221
[6] ISOLATED SINGULARITIES OF SOME SEMILINEAR ELLIPTIC-EQUATIONS
VAZQUEZ, JL
VERON, L
JOURNAL OF DIFFERENTIAL EQUATIONS, 1985, 60 (03) : 301 - 321
[7] Removability of an isolated singularity for anisotropic elliptic equations with absorption
Skrypnik, I. I.
SBORNIK MATHEMATICS, 2008, 199 (7-8) : 1033 - 1050
[8] SEMILINEAR ELLIPTIC SYSTEM WITH BOUNDARY SINGULARITY
Li, Yimei
Bao, Jiguang
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (04) : 2189 - 2212
[9] Removability of an isolated singularity of solutions of nonlinear elliptic equations with absorption
Skrypnik I.I.
Ukrainian Mathematical Journal, 2005, 57 (7) : 1149 - 1166
[10] Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent
Liao, Jia-Feng
Liu, Jiu
Zhang, Peng
Tang, Chun-Lei
ANNALES POLONICI MATHEMATICI, 2016, 116 (03) : 273 - 292

← 1 2 3 4 5 →