Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 147, pp. 1-18.

Title: Uniqueness and asymptotic behavior of boundary blow-up solutions 
       to semilinear elliptic problems with non-standard growth

Authors: Shuibo Huang (Lanzhou Univ., Gansu, China)
         Wan-Tong Li  (Lanzhou Univ., Gansu, China)
	 Qiaoyu Tian  (Gansu Normal Univ. China)

Abstract:
 In this article, we analyze uniqueness and asymptotic behavior
 of boundary blow-up non-negative solutions to the semilinear elliptic equation
 $$\displaylines{
 \Delta u=b(x)f(u),\quad x\in \Omega,\cr
 u(x)=\infty, \quad x\in\partial\Omega,
 }$$
 where $\Omega\subset\mathbb{R}^N$ is a bounded smooth domain,
 b(x) is a non-negative function on $\Omega$ and f is non-negative on
 $[0,\infty)$ satisfying some  structural conditions.  The main novelty
 of this paper is that uniqueness is established only by imposing
 a control on their growth on the weights b(x) near $\partial\Omega$
 and the nonlinear term f at infinite, rather than requiring them to
 have a precise asymptotic behavior. Our proof is based on the
 method of sub and super-solutions and the Safonov iteration technique.

Submitted July 20, 2012. Published August 21, 2012.
Math Subject Classifications: 35J65, 35J60, 74G30, 35B40.
Key Words: Boundary blow-up solutions; uniqueness; asymptotic behavior.