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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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