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.