Large and small solutions of a class of quasilinear elliptic eigenvalue problems
type: Item
instance of: scholarly article
title: Large and small solutions of a class of quasilinear elliptic eigenvalue problems
zbMATH Open document ID: 1014.35030
author: Zongming Guo
author: J. Webb
published in: Journal of Differential Equations
publication date: 2002-09-08T00:00:00Z
review text: The authors deal with the existence of positive solutions of the quasilinear eigenvalue problem \[ \begin{cases} -\Delta_p u=\lambda f(u)\quad & \text{in }\Omega,\\ u=0\quad & \text{on }\partial \Omega,\end{cases} \tag{1} \] where \(1<p< \infty\), \(\lambda>0\). Under some suitable assumptions on \(f\), the authors obtain existence and uniqueness results for large positive solutions for (1). To this end they use mountain pass arguments and show that this solution develops to a spike layer solution.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35P30
zbMATH DE Number: 1797533
zbMATH Keywords: spike layer solition
zbMATH Keywords: positive solutions
zbMATH Keywords: mountain pass arguments
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jdeq.2001.4049
OpenAlex ID: W1969014187
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DOI: 10.1006/JDEQ.2001.4049
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description: scientific article; zbMATH DE number 1797533