The asymptotic behaviour of solutions with boundary blow-up for semilinear elliptic equations with nonlinear gradient terms

In this paper, we show existence, uniqueness and exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems Δu±λ|∇u|q=k(x)g(u), x∈Ω, u|∂Ω=+∞, where Ω is a bounded domain with smooth boundary in RN, λ⩾0, q∈[0,2], limd(x)→0k(x)dσ(x)=c0, 0⩽σ<2, c0>0, g∈C1[0,∞), g(0)=0, g is increasing on (0,∞), and is Karamata regular variation function at infinity with index 1+ρ and ρ>0.