带有负指数 Kirchhoff 方程稳定解的Liouville型定理

In this paper, we consider the Liouville-type theorem for stable solutions of the following Kirchhoff equation ■,where M(t) = a + bt~θ, a 0, b, θ≥ 0, θ = 0 if and only if b = 0. N ≥ 2, q 0 and the nonnegative function g(x) ∈ L_(loc)~1(R~N). Under suitable conditions on g(x), θ and q, we investigate the nonexistence of positive stable solution for this problem.

Liouville-Type Theorem for Stable Solutions of the Kirchhoff Equation with Negative Exponent

In this paper, we consider the Liouville-type theorem for stable solutions of the following Kirchhoff equation $$M\Big(\int_{\mathbb{R}^N}|\nabla u|^2\d x\Big)\Delta u=g(x)u^{-q},\ \ x\in \mathbb{R}^N, $$ where $M(t)=a+bt^{\theta}, a>0, b, \theta\ge0, \theta=0$ if and only if $b=0$. $N\geq2, q>0$ and the nonnegative function $g(x)\in L^{1}_{{\rm loc}}(\mathbb{R}^N)$. Under suitable conditions on $g(x), \theta$ and $q$, we investigate the nonexistence of positive stable solution for this problem.