Bandle, Catherine; Marcus, Moshe On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems. (English) Zbl 1042.35535 Differ. Integral Equ. 11, No. 1, 23-34 (1998). Let \(D\) be a bounded smooth domain in \(\mathbb R^N\). It is well known that large solutions of an equation such as \(\Delta u = u^p\), \(p>1\) in \(D\) blow up at the boundary at a rate \(\phi (\delta )\) which depends only on \(p\). (Here \(\delta (x)\) denotes the distance of \(x\) to the boundary.) In this paper the authors consider a secondary effect in the asymptotic behaviour of solutions, namely, the behaviour of \(u/\phi (\delta ) - 1\) as \(\delta \rightarrow 0\). They derive estimates for this expression, which are valid for a large class of nonlinearities and extend a recent result of Lazer and McKenna. Reviewer: Pavel Drábek (Plzeň) Cited in 1 ReviewCited in 63 Documents MSC: 35J60 Nonlinear elliptic equations 34C99 Qualitative theory for ordinary differential equations 35B40 Asymptotic behavior of solutions to PDEs PDFBibTeX XMLCite \textit{C. Bandle} and \textit{M. Marcus}, Differ. Integral Equ. 11, No. 1, 23--34 (1998; Zbl 1042.35535)