Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear problems
type: Item
instance of: scholarly article
title: Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear problems
zbMATH Open document ID: 0607.34012
DOI: 10.1016/0022-0396(87)90035-0
author: Hans-Peter Heinz
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: The discussion in this paper centers around the singular nonlinear Dirichlet problem \(-u''+w(t)| u|^{\sigma}u=\lambda u,\) \(u(0)=0\), \(u\in L^ 2[0,\infty)\), where \(\sigma >0\) is a constant, and w is a positive continuous function satisfying the minimal growth condition \(\int^{\infty}_{0}w^{-2/\sigma}dt<\infty.\) After some remarks on free Ljusternik-Schnirelman theory, the author gives applications to abstract nonlinear eigenvalue problems, semilinear elliptic boundary value problems, and to bifurcation theory.
reviewed by: N.L.Maria
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 3981572
zbMATH Keywords: second order differential equation
zbMATH Keywords: singular nonlinear Dirichlet problem
zbMATH Keywords: applications
zbMATH Keywords: abstract nonlinear eigenvalue problems
zbMATH Keywords: semilinear elliptic boundary value problems
zbMATH Keywords: bifurcation
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90035-0
OpenAlex ID: W2015791504
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description: scientific article; zbMATH DE number 3981572