Boundary behavior of large solutions for semilinear elliptic equations in borderline cases

In this article, we analyze the boundary behavior of solutions to the boundary blow-up elliptic problem $$ Delta u =b(x)f(u), quad ugeq 0,; xinOmega,; u|_{partial Omega}=infty, $$ where $Omega$ is a bounded domain with smooth boundary in $mathbb{R}^N$, $f(u)$ grows slower than any $u^p$ ($p > 1$) at infinity, and $b in C^{alpha}(ar{Omega})$ which is non-negative in Omega and positive near $partialOmega$, may be vanishing on the boundary.