Global bifurcation in \(2m\)-order generic systems of nonlinear boundary value problems
type: Item
instance of: scholarly article
title: Global bifurcation in \(2m\)-order generic systems of nonlinear boundary value problems
zbMATH Open document ID: 1260.34030
DOI: 10.1155/2012/804619
author: Xiaoling Han
author: Jia Xu
author: Guowei Dai
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: We consider the system \[ \begin{aligned} (-1)^m u^{(2m)} &= \lambda u + \lambda v + uf(t, u, v),\quad t \in (0, 1),\\ u^{(2i)}(0)& = u^{(2i)}(1) = 0,\quad 0 \leq i \leq m - 1,\\ (-1)^m v^{(2m)}& = \mu u + \mu v + vg(t, u, v),\quad t \in (0, 1),\\ v^{(2i)}(1)& = 0,\quad 0 \leq i \leq m - 1,\end{aligned} \] where \(\lambda, \mu \in \mathbb R\) are real parameters. \(f, g : [0, 1] \times \mathbb R^2 \rightarrow \mathbb R\) are \(C^k,\;k \geq 3\) functions and \(f(t, 0, 0) \equiv g(t, 0, 0) \equiv 0,\;t \in [0, 1]\). It is shown that, if the functions, \(f\) and \(g\) are ``generic'', then the solution set of the system consists of a countable collection of two-dimensional \(C^k\) manifolds.
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 6134166
Wikidata QID: Q58696828
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/804619
OpenAlex ID: W2069025677
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description: scientific article; zbMATH DE number 6134166