Analysis of a bifurcation problem
type: Item
instance of: scholarly article
title: Analysis of a bifurcation problem
zbMATH Open document ID: 0997.65084
DOI: 10.1016/S0378-4754(01)00366-4
published in: Mathematics and Computers in Simulation
publication date: 2002-05-21T00:00:00Z
review text: A bifurcation problem of the type \(u-\lambda Lu+g(\lambda,u,y)=0\) in a neighborhood of a particular solution \((\lambda_0,0,0)\in \mathbb{R}\times E\times F\) is considered. Here \(E, F\) are real Banach spaces and \(\lambda_0\) is a semisimple characteristic number of the linear operator \(L\). Under certain assumptions about the perturbating nonlinearity the authors prove the existence of a bifurcation. The main results of the article consist in the application of Galerkin's method to reduce the space. Numerical results are discussed.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J15
zbMATH DE Number: 1743081
zbMATH Keywords: bifurcation
zbMATH Keywords: Lyapounov-Schmidt reduction
zbMATH Keywords: Galerkin's method
zbMATH Keywords: Banach spaces
zbMATH Keywords: numerical results
author: Said El Hajji
author: Mohammed Errachid
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
cites work: Q5635885
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cites work: Bifurcation of operator equations with unbounded linearized part
full work available at URL: s0378-4754(01)00366-4
OpenAlex ID: W2028199963
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description: scientific article; zbMATH DE number 1743081