Scaling solution branches of one-parameter bifurcation problems
type: Item
instance of: scholarly article
title: Scaling solution branches of one-parameter bifurcation problems
zbMATH Open document ID: 0873.35008
author: A. Schwarzer
author: Zhen Mei
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-10-05T00:00:00Z
review text: The authors study an abstract one-parameter bifurcation problem and, in order to investigate the steady state and the Hopf bifurcations, they apply the Lyapunov-Schmidt reduction method for obtaining an equivalent lower dimensional system of algebraic equations. They use the Böhmer-Mei method for exploiting the scales of solution branches and unify the two succesive steps in the standard Lyapunov-Schmidt method. It is also defined an algorithm for analyzing the bifurcation structure and for the branch switching in solution branches of the considered problem. As an application, there are studied bifurcations of a semilinear elliptic problem on square or hexagonal domains. There are also found numerical values of the coefficients in the reduced bifurcation equations on these domains.
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 58E09
Mathematics Subject Classification ID: 35C10
zbMATH DE Number: 1005487
zbMATH Keywords: Lyapunov-Schmidt method
zbMATH Keywords: Taylor series
zbMATH Keywords: branch switching
zbMATH Keywords: semilinear elliptic problem on square or heagonal domains
zbMATH Keywords: reduced bifurcation equations
reviewed by: Vicenţiu D. Rădulescu
MaRDI profile type: Publication
OpenAlex ID: W2060834047
DOI: 10.1006/JMAA.1996.0426
description: scientific article; zbMATH DE number 1005487