Liouville-type theorems for stable solutions of singular quasilinear elliptic equations in R^N

We prove a Liouville-type theorem for stable solution of the singular quasilinear elliptic equations $$\displaylines{ -\text{div}(|x|^{-ap}|\nabla u|^{p-2}\nabla u)=f(x)|u|^{q-1}u, \quad \text{in } \mathbb{R}^N, \cr -\text{div}(|x|^{-ap}|\nabla u|^{p-2}\nabla u)=f(x)e^u, \quad \text{in } \mathbb{R}^N }$$ where $2\le p