Asymptotic behavior and uniqueness of boundary blow-up solutions to elliptic equations. (English) Zbl 1324.35044

Tian, Qiaoyu; Xu, Yonglin

Electron. J. Qual. Theory Differ. Equ. 2014, Paper No. 73, 10 p. (2014).

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

Keywords:

boundary blow-up solutions; asymptotic behavior; López-Gómez localization method; Karamata regular variation theory