  We provide sufficient conditions on $w\in L^1_{loc}(\mathbb{R}^N)$ such that
the weighted $p$-Laplace equation $$-\operatorname{div}\big(w(x)|\nabla
u|^{p-2}\nabla u\big)=f(u)\;\;\mbox{in}\;\;\mathbb{R}^N$$ does not admit any
stable $C^{1,\zeta}_{loc}$ solution in $\mathbb{R}^N$ where $f(x)$ is either
$-x^{-\delta}$ or $e^x$ for any $0<\zeta<1$.
