%0 Journal Article
%T Uniqueness and asymptotic behavior of boundary blow-up solutions to semilinear elliptic problems with non-standard growth
%A Shuibo Huang
%A Wan-Tong Li
%A Qiaoyu Tian
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X In this article, we analyze uniqueness and asymptotic behavior of boundary blow-up non-negative solutions to the semilinear elliptic equation $$displaylines{ Delta u=b(x)f(u),quad xin Omega,cr u(x)=infty, quad xinpartialOmega, }$$ where $Omegasubsetmathbb{R}^N$ 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 $partialOmega$ 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.
%K Boundary blow-up solutions
%K uniqueness
%K asymptotic behavior
%U http://ejde.math.txstate.edu/Volumes/2012/147/abstr.html