Some elliptic problems with singular natural growth lower order terms

In this paper we deal with a nonlinear elliptic problem, whose model is{−Δu=B|Du|2u+finΩ,u=0on∂Ω, where B>0B>0 and f⩾0f⩾0 belongs to a Lebesgue space. We prove the existence of positive solutions in suitable Sobolev spaces (depending on f and B).