含Grushin梯度的加权m-Laplace方程稳定解的Liouville定理  

Liouville type theorems for stable solutions of the weighted m-Laplace equation with Grushin gradient

作　　者：邱佳露 胡良根 QIU Jiau;HU Lianggen(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报(理工版)》2025年第2期109-114,共6页Journal of Ningbo University:Natural Science and Engineering Edition

基　　金：宁波市自然科学基金(2023J127).

摘　　要：研究了含Grushin梯度加权m-Laplace方程-▽_(G)(|▽_(G)u|^(m-2)▽_(G)u)+||X||^(θ)|u|^(p-1)u=||X||^(δ)|u|^(q-1)u,其中▽_(G)=(▽_(x),|x|^(α)▽_(y))是Grushin梯度,α>0,m≥2,X=(x,y)∈R^(N)=R^(N_(1))×R^(N_(2)),||X||=(|x|^(2(a+1))+|y|^(2))^(1/(2(a+1))).采用Moser迭代、积分估计等方法,探讨θ、δ、p、q取不同值,齐次维数N_(α)=N_(1)+(1+α)N_(2)取不同上界值时,建立m-Laplace方程稳定解的Liouville定理.In the paper,the weighted m-Laplace equation with Grushin gradient is considered-▽_(G)(|▽_(G)u|^(m-2)▽_(G)u)+||X||^(θ)|u|^(p-1)u=||X||^(δ)|u|^(q-1)u where▽_(G)=(▽_(x),|x|^(α)▽_(y))is Grushin gradient,α>0,m≥2,X=(x,y)∈R^(N)=R^(N_(1))×R^(N_(2)),||X||=(|x|^(2(a+1))+|y|^(2))^(1/(2(a+1))).By employing Moser iteration and integral estimate,the Liouville type theorems of stable solution for m-Laplace equation is established,whenθ,δ,p,q take different values and the homogeneous dimension N_(α)=N_(1)+(1+α)N_(2)takes different upper bound values.

关 键 词：Grushin梯度 权项 稳定解 LIOUVILLE定理 

分 类 号：O186[理学—数学]