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 egin{equation*} egin{cases} Delta u=b(x)f(u), &xin Omega, u(x)=infty, &xinpartialOmega, end{cases} end{equation*} where $Omegasubsetmathbb{R}^N$ is a bounded smooth domain. Our analysis is based on the Karamata regular variation theory and López-Gómez localization method.
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机译：在本文中，在权重函数$ b（x）$和非线性项$ f（u）$的一些结构假设下，我们建立了半线性椭圆型方程 begin {equation *}的边界爆破解的渐近行为和唯一性 begin {cases} Delta u = b（x）f（u），＆x in Omega， u（x）= infty，＆x in partial Omega， end {cases} end { equation *}，其中$ Omega subset mathbb {R} ^ N $是有界平滑域。我们的分析基于Karamata正则变分理论和López-Gómez定位方法。
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