Asymptotic behavior up to the second order term of solutions to quasilinear elliptic singular problems

Let Ω⊂RNΩ⊂RN be a bounded smooth domain. We prove the existence of a positive solution to the problem Δu=−u−γ|∇u|qΔu=−u−γ|∇u|q in ΩΩ, u=0u=0 on ∂Ω∂Ω, with γ>1γ>1 and 03γ>3 and 0