A boundary blow-up for a class of quasilinear elliptic problems with a gradient term

By a perturbation method and constructing comparison functions, we show the exact asymptotic behavior of solutions near the boundary to quasilinear elliptic problem $$\left\{\begin{array}{ll}\mbox{div}\left(|\nabla u|^{m-2}\nabla u\right)-|\nabla u(x)|^{q(m-1)}=b(x)g(u),\quad x\in \Omega,\\u>0,\quad x\in \Omega,\\u|_{\partial\Omega}=+\infty,\end{array}\right.$$ where Ω is a C ² bounded domain with smooth boundary, m>1,q∈(1,m/(m?1)], g∈C0,∞)∩C ¹(0,∞), g(0)=0, g is increasing on 0,∞), and b is non-negative and non-trivial in Ω, which may be singular on the boundary.