Boundary blow-up quasilinear elliptic problems of the Bieberbach type with nonlinear gradient terms

By a perturbation method and by constructing comparison functions, we show the exact asymptotic behaviour of solutions near the boundary of the quasilinear elliptic problem {div(|∇u|m−2∇u)±|∇u(x)|q(m−1)=b(x)eu(x),x∈Ω,u|∂Ω=+∞, where ΩΩ is a C2C2 bounded domain with a smooth boundary in RN(N≥2),m>1,q≥0,b is nonnegative and nontrivial in ΩΩ, which may vanish on the boundary.