Non-existence results for the weighted $p$-Laplace equation with singular nonlinearities

In this paper we present some non existence results concerning the stable solutions to the equation $$\mathrm{div}(w(x)\mathrm{\mid }\mathrm{\nabla }u{\mathrm{\mid }}^{p-2}\mathrm{\nabla }u)=g(x)f(u)in{\mathbb{R}}^N;p\ge 2$$ when $f(u)$ is either $u^{-\delta }+u^{-\gamma }$, $\delta ,\gamma >0$ or $\exp (\frac{1}{u})$ and for a suitable class of weight functions $w,g$.