Singular quasilinear equations with quadratic growth in the gradient without sign condition

Given a bounded domain Ω   in RNRN, and a function a∈Lq(Ω)a∈Lq(Ω) with q>N/2q>N/2, we study the existence of a positive solution for the quasilinear problem−Δw+g(x,w)|∇w|2=a(x),x∈Ω,w∈H01(Ω), where g(x,s)g(x,s) is a Carathéodory function on Ω×(0,+∞)Ω×(0,+∞) which may have a singularity at s=0s=0 and may change of sign.