Nonexistence results for weighted p-Laplace equations with singular nonlinearities

Abstract

In this article we present some nonexistence results concerning stable solutions to the equation $$ \hbox{div}\big(w(x)|\nabla u|^{p-2}\nabla u\big) =g(x)f(u)\quad \text{in }\mathbb{R}^N,\;p\geq 2 $$ when f(u) is either $u^{-\delta}+u^{-\gamma}$ with $\delta,\gamma>0$ or $e^{1/u}$ where w,g are suitable weight functions.

Keywords

• p-Laplacian
• nonexistence
• stable solution