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

Abstract

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.

Keywords

• boundary blow-up solutions
• asymptotic behavior
• lópez-gómez localization method
• karamata regular variation theory