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

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 term. We use an adequate sub-super-solution method to prove the existence of solutions, the characterization of eigenvalues and the integrability of the term |∇u|2/u2 for the non-existence and results from Arcoya-Segura de León for the uniqueness.