By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem △u=k(x)g(u), u>0, x in Omega,
u|_{\partial \Omega}=+∞, where Omega is a bounded domain with smooth boundary in R^N; g ∈ C¹[0,∞), g(0)=g'(0)=0, and there exists p>1, such that $\lim\limits_{s\rightarrow \infty}\frac {g(s \xi)}{g(s)}=\xi^p$, $\forall \ \xi>0$, and $k \in C_{\rm loc}^\alpha(\Omega)$ is non-negative non-trivial in Omega which may be singular on the boundary.