Liouville Results for Stable Solutions of Quasilinear Equations with Weights

This paper is devoted to the quasilinear equation

where  is a (bounded or unbounded) domain of  are nonnegative continuous functions and  is an increasing function. We establish a Liouville type theorem for nontrivial stable solutions of the equation under some mild assumptions on  and , which extends and unifies several results on this topic.