Existence and non-existence of positive solutions for nonlinear elliptic singular equations with natural growth

Abstract

In this paper we analyze the existence, non-existence and uniqueness of positive solutions of some nonlinear elliptic equations containing singular terms and natural growth in the gradient. We use an adequate sub-supersolution method to prove the existence of solutions, different arguments for the nonexistence and results from Arcoya-Segura de Le´on for the uniqueness.