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Asymptotic behavior and uniqueness of boundary blow-up solutions to elliptic equations. (English) Zbl 1324.35044
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 $\Delta u=b(x)f(u), x\in \Omega,$ $u(x)=\infty, x\in\partial\Omega,$ 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.
##### MSC:
 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian 35B40 Asymptotic behavior of solutions to PDEs 35B44 Blow-up in context of PDEs
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