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

Abstract

In this paper we present some non existence results concerning the stable solutions to the equation $$\operatorname{div}(w(x)|\nabla u|^{p-2}\nabla u)=g(x)f(u)\;\;\mbox{in}\;\;\mathbb{R}^N;\;\;p\geq 2$$ when $f(u)$ is either $u^{-\hat{I}´}+u^{-{\hat{I}}^3}$, $\hat{I}´,{\hat{I}}^3>0$ or $\exp (\frac{1}{u})$ and for a suitable class of weight functions $w,g$.