Equivariant bifurcation index
type: Item
instance of: scholarly article
title: Equivariant bifurcation index
zbMATH Open document ID: 1207.37040
author: Gabriel López Garza
author: Sławomir Maciej Rybicki
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-09-10T00:00:00Z
review text: A bifurcation index \({\mathcal B}l{\mathcal F}_G(v^{-1}_{k_0})\in U(G)\) defined in terms of the degree for \(G\)-equivariant gradient maps, where \(G\) is real, compact, connected Lie group and \(U(G)\) is the Euler ring of \(G\), is considered. The main result is the following: \[ {\mathcal B}l{\mathcal F}_G(v^{-1}_{k_0})\neq \Theta\in U(G)\text{ iff }{\mathcal B}l{\mathcal F}_T(v^{-1}_{k_0})\neq\Theta\in U(T), \] where \(T\subset G\) is a maximal torus of \(G\). Applications of global bifurcations of weak solutions of elliptic differential equations are considered.
Mathematics Subject Classification ID: 37G40
Mathematics Subject Classification ID: 58E09
zbMATH DE Number: 5782205
zbMATH Keywords: equivariant gradient degree
zbMATH Keywords: compact Lie group
zbMATH Keywords: symmetry breaking
zbMATH Keywords: elliptic PDE
reviewed by: A. P. Sadovskiĭ
MaRDI profile type: Publication
full work available at URL: j.na.2010.06.001
OpenAlex ID: W2053833276
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DOI: 10.1016/J.NA.2010.06.001
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