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

共 50 条

[1] Blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term
Ghoul, Tej-Eddine
Van Tien Nguyen
Zaag, Hatem
JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (08) : 4517 - 4564
[2] Singular solutions of a p-Laplace equation involving the gradient
Cowan, C.
Razani, A.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (04) : 3914 - 3942
[3] Entire positive solutions of the singular Emden-Fowler equation with nonlinear gradient term
Teodora-Liliana Dinu
Results in Mathematics, 2003, 43 (1-2) : 96 - 100
[4] CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT
Xu Youjun
Liu Zhenhai
ACTA MATHEMATICA SCIENTIA, 2010, 30 (05) : 1593 - 1604
[5] Controllability for a parabolic equation with a nonlinear term involving the state and the gradient
Xu Y.
Li J.
Liu Z.
Journal of Applied Mathematics and Computing, 2009, 29 (1-2) : 197 - 206
[6] CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT
许友军
刘振海
Acta Mathematica Scientia, 2010, 30 (05) : 1593 - 1604
[7] STABILIZATION OF SOLUTIONS OF A NONLINEAR PARABOLIC EQUATION WITH A GRADIENT TERM
DENG, K
MATHEMATISCHE ZEITSCHRIFT, 1994, 216 (01) : 147 - 155
[8] Singular solutions of elliptic equations involving nonlinear gradient terms on perturbations of the ball
Aghajani, A.
Cowan, C.
Lui, S. H.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (04) : 2865 - 2896
[9] Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient
Bodart, O
González-Burgos, M
Pérez-García, R
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 57 (5-6) : 687 - 711
[10] EXISTENCE AND CLASSIFICATION OF SINGULAR SOLUTIONS TO NONLINEAR ELLIPTIC EQUATIONS WITH A GRADIENT TERM
Ching, Joshua
Cirstea, Florica
ANALYSIS & PDE, 2015, 8 (08): : 1931 - 1962

← 1 2 3 4 5 →