A complete classification of bifurcation diagrams of classes of multiparameter \(p\)-Laplacian boundary value problems
type: Item
instance of: scholarly article
title: A complete classification of bifurcation diagrams of classes of multiparameter \(p\)-Laplacian boundary value problems
zbMATH Open document ID: 1175.34018
author: Kuo-Chih Hung
author: Shin-Hwa Wang
published in: Journal of Differential Equations
publication date: 2009-03-17T00:00:00Z
review text: Earlier the second author and \textit{T.-S. Yeh} [Nonlinear Anal., Theory Methods Appl. 64, 2412--2432 (2006; Zbl 1096.34014)] gave a complete classification of bifurcation diagrams of positive solutions of the problem \[ (|u'|^{p-2}u')'+f(u)=0,\quad u(-1)=u(1)=0 \] in the case \(f(u)=\lambda g(u)+h(u)\), where \(\lambda >0\) is a bifurcation parameter. In this paper, the authors give a similar analysis in the more general case \(f(u)=g(u,\lambda )+h(u,\mu )\), where \(\lambda\) and \(\mu\) are bifurcation parameters. Under appropriate conditions, they give a classification of eight qualitatively different bifurcation diagrams. They also establish the exact multiplicity of positive solutions.
reviewed by: Alan L. Andrew
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 5529542
zbMATH Keywords: bifurcation diagram
zbMATH Keywords: positive solution
zbMATH Keywords: multiparameter problem
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: multiplicity
MaRDI profile type: Publication
full work available at URL: j.jde.2008.10.035
OpenAlex ID: W2015789600
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DOI: 10.1016/J.JDE.2008.10.035
description: scientific article; zbMATH DE number 5529542