Bifurcation solution branches and their numerical approximations of a semi-linear elliptic problem with two parameters
type: Item
instance of: scholarly article
title: Bifurcation solution branches and their numerical approximations of a semi-linear elliptic problem with two parameters
zbMATH Open document ID: 0938.65105
DOI: 10.1007/BF02677404
author: Heyuan Wang
author: Kaitai Li
author: A. X. Huang
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2000-06-28T00:00:00Z
review text: In the interval \((0,\pi)\), the authors consider the boundary value problem \[ u''+(\lambda+ s(\mu)) f(u)- \mu\sin x= 0,\quad u(0)= u(\pi)= 0. \] Here, \(\lambda\) and \(\mu\) are real parameters and \(f\), \(s\) smooth odd functions satisfying certain conditions. Due to \(f(0)= 0\), the problem has in particular the trivial solution \(u= 0\), \(\mu=0\), \(\lambda\in\mathbb{R}\). In the special case \(\mu= 0\), bifurcation from the trivial solution has been studied among others by \textit{E. I. Allgower}, \textit{K. Böhmer} and \textit{Z. Mei} [IMA J. Numer. Anal. 14, No. 2, 161-182 (1994; Zbl 0803.65103)]. Starting from known branching solutions of the special problem, the present authors apply continuation methods in order to find solutions for given values of the parameters \(\lambda\) and \(\mu\). Theoretical and numerical results are presented.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L16
Mathematics Subject Classification ID: 34L30
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1340727
zbMATH Keywords: semilinear elliptic problem
zbMATH Keywords: bifurcation
zbMATH Keywords: branching solutions
zbMATH Keywords: continuation methods
zbMATH Keywords: numerical results
reviewed by: Waldemar Velte
MaRDI profile type: Publication
cites work: Branch switching at a corank-4 bifurcation point of semi-linear elliptic problems with symmetry
cites work: The numerical treatment of non-trivial bifurcation points
cites work: Bifurcation from simple eigenvalues
full work available at URL: https://doi.org/10.1007/bf02677404
OpenAlex ID: W2078807019
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description: scientific article; zbMATH DE number 1340727