Boundary behavior of large solutions to semilinear elliptic equations with nonlinear gradient terms

In this paper, we study the boundary behavior of solutions to boundary blow-up elliptic problems △u±|∇u|q=b(x)f(u),x∈Ω,u|∂Ω=+∞, where ΩΩ is a bounded domain with smooth boundary in RNRN, q>0q>0, b∈Cα(Ω̄), which is positive in ΩΩ and may be vanishing on the boundary and rapidly varying near the boundary, and ff is rapidly varying or normalized regularly varying at infinity.