【摘要】 研究了含Grushin梯度加权m-Laplace方程■,其中▽_G=（▽_x,|x|^α▽_y）是Grushin梯度,α>0,m≥2,■.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=N₁+（1+α）N₂取不同上界值时,建立m-Laplace方程稳定解的Liouville定理.更多还原

【Abstract】 In the paper, the weighted m-Laplace equation with Grushin gradient is considered ■ where ▽_G=（▽_x,|x|^α▽_y） is Grushin gradient, α>0, m≥2,■. By employing Moser iteration and integral estimate, the Liouville type theorems of stable solution for m-Laplace equation is established, when θ, δ, p, q take different values and the homogeneous dimension N_α=N₁+（1+α）N₂ takes different upper bound values.更多还原