Asymptotic behavior and uniqueness of boundary blow-up solutions to elliptic equations

In this paper, under some structural assumptions of weight function $b(x)$ and nonlinear term $f(u)$, we establish the asymptotic behavior and uniqueness of boundary blow-up solutions to semilinear elliptic equations \begin{equation*} \begin{cases} \Delta u=b(x)f(u), &x\in \Omega,\\ u(x)=\infty,...

Full description

Saved in:
Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2014-01, Vol.2014 (73), p.1-10
Main Authors: Tian, Qiaoyu, Xu, Yonglin
Format: Article
Language:English
Subjects:
asymptotic behavior
boundary blow-up solutions
karamata regular variation theory
lópez-gómez localization method
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, under some structural assumptions of weight function $b(x)$ and nonlinear term $f(u)$, we establish the asymptotic behavior and uniqueness of boundary blow-up solutions to semilinear elliptic equations \begin{equation*} \begin{cases} \Delta u=b(x)f(u), &x\in \Omega,\\ u(x)=\infty, &x\in\partial\Omega, \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^N$ is a bounded smooth domain. Our analysis is based on the Karamata regular variation theory and López-Gómez localization method.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2014.1.73