Structure of boundary blow-up solutions for quasi-linear elliptic problems. II: Small and intermediate solutions
type: Item
instance of: scholarly article
title: Structure of boundary blow-up solutions for quasi-linear elliptic problems. II: Small and intermediate solutions
zbMATH Open document ID: 1134.35339
author: Zongming Guo
author: J. Webb
published in: Journal of Differential Equations
publication date: 2005-04-18T00:00:00Z
review text: Let \(\Omega\subset \mathbb R^N\) be a bounded smooth domain. The authors deal with a boundary blow-up solutions of the problem \[ \begin{gathered} -\Delta_p u=\lambda f(u)\quad\text{in }\Omega,\\ u|_{\partial\Omega}= \infty,\end{gathered}\tag{1} \] where \(\lambda> 0\) is a parameter, \(\Delta_pu= \text{div}(|Du|^{p-2} Du)\) with \(1<p<\infty\) is the \(p\)-Laplacian. Under natural assumptions on \(f(s)\) the authors discuss the structure of small and intermediate solutions of (1). They show that, for sufficiently large \(\lambda\), the equation (1) has a unique small solution and infinitely many intermediate solutions. It is important to emphasize that, in contrast to previous results, a strong monotone assumption on the nonlinearity was not imposed. Part I, see Proc. R. Soc. Edinb., Sect. A, Math. 135, No. 3, 615--642 (2005; Zbl 1129.35381).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 2157588
zbMATH Keywords: Quasi-linear elliptic problems
zbMATH Keywords: Boundary-layer solutions
zbMATH Keywords: Spike-layer solutions
zbMATH Keywords: Uniqueness
zbMATH Keywords: Boundary layer estimates
MaRDI profile type: Publication
full work available at URL: j.jde.2004.06.008
OpenAlex ID: W2054159656
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DOI: 10.1016/J.JDE.2004.06.008
description: scientific article; zbMATH DE number 2157588