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.
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页码：141 / 158
页数：18
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