SINGULAR SOLUTIONS OF A HENON EQUATION INVOLVING A NONLINEAR GRADIENT TERM

被引：6

作者：

Cowan, Craig ^{[1
]}

Razani, Abdolrahman ^{[2
]}

机构：

[1] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

[2] Imam Khomeini Int Univ, Fac Sci, Dept Pure Math, Qazvin 3414916818, Iran

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2022年 / 21卷 / 01期

关键词：

Henon equation; singular solutions; Laplace equation involving the gradient term; semilinear elliptic equations; perturbations of nonlinear operators; ELLIPTIC PROBLEMS; EXISTENCE; GROWTH;

D O I：

10.3934/cpaa.2021172

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Here, we consider positive singular solutions of {-Delta u = vertical bar x vertical bar(alpha) vertical bar del u vertical bar(p) in Omega\{0}, u=0 on partial derivative Omega, where Omega is a small smooth perturbation of the unit ball in R-N and a and p are parameters in a certain range. Using an explicit solution on B-1 and a linearization argument, we obtain positive singular solutions on perturbations of the unit ball.

引用

页码：141 / 158

页数：18

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