Electron. J. Diff. Equ., Vol. 2012 (2012), No. 136, pp. 1-11.

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

Zhijun Zhang

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.

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Zhijun Zhang
School of Mathematics and Information Science
Yantai University
Yantai, Shandong, 264005, China
email: zhangzj@ytu.edu.cn, chinazjzhang@yahoo.com.cn

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