Two global several-parameter bifurcation theorems and their applications
type: Item
instance of: scholarly article
title: Two global several-parameter bifurcation theorems and their applications
zbMATH Open document ID: 1339.47078
author: Guowei Dai
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-09-30T00:00:00Z
review text: This paper deals with the study of the nonlinear operator equation \[ u=L(\lambda)u+H(\lambda ,u),\quad u\in X, \] where \(X\) is a real Banach space, \(\lambda\in {\mathbb R}^m\), and \(L,H\) are continuous operators. The main result of this paper establishes a global bifurcation property, provided that \(L\) is a positively homogeneous completely continuous operator. In the case when \(L\) is a homogeneous completely continuous operator, it is established a unilateral global bifurcation result. A key role in the proofs is played by the Rabinowitz global bifurcation theorem in combination with topological degree arguments.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 47J15
Mathematics Subject Classification ID: 35J92
zbMATH DE Number: 6487281
zbMATH Keywords: global bifurcation
zbMATH Keywords: several-parameter
zbMATH Keywords: Fučik spectrum
MaRDI profile type: Publication
full work available at URL: j.jmaa.2015.08.035
OpenAlex ID: W1472152530
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DOI: 10.1016/J.JMAA.2015.08.035
description: scientific article; zbMATH DE number 6487281