Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 136, pp. 1-11.

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

Author: Zhijun Zhang (Yantai Univ., Shandong, China)

Abstract:
 In this article, we analyze  the boundary  behavior of solutions to
 the  boundary blow-up  elliptic problem
 $$
 \Delta u =b(x)f(u), \quad u\geq 0,\; x\in\Omega,\; 
 u|_{\partial \Omega}=\infty,
 $$
 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
 $b \in C^{\alpha}(\bar{\Omega})$ which is non-negative in 
 \Omega
 and positive near $\partial\Omega$, may be vanishing on the boundary.
 
Submitted June 30, 2012. Published August 19, 2012.
Math Subject Classifications: 35J55, 35J60, 35J65.
Key Words: Semilinear elliptic equations;  boundary blow-up;
           boundary  behavior; borderline cases.