A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation

We consider a nonlinear equation F(ε,λ,u)=0, where the parameter ε is a perturbation parameter, F is a differentiable mapping from R×R×X to Y, and X, Y are Banach spaces. We obtain an abstract bifurcation theorem by using the generalized saddle-node bifurcation theorem.

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Main Authors: Ping Liu, Yuwen Wang
Format: Article
Language:English
Published: Wiley 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/302942
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author Ping Liu
Yuwen Wang
author_facet Ping Liu
Yuwen Wang
author_sort Ping Liu
collection DOAJ
description We consider a nonlinear equation F(ε,λ,u)=0, where the parameter ε is a perturbation parameter, F is a differentiable mapping from R×R×X to Y, and X, Y are Banach spaces. We obtain an abstract bifurcation theorem by using the generalized saddle-node bifurcation theorem.
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issn 1085-3375
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publishDate 2011-01-01
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series Abstract and Applied Analysis
spelling doaj-art-53caadc1a21043cfa18e397faeb3517a2025-08-20T02:05:24ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/302942302942A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear EquationPing Liu0Yuwen Wang1Y.Y. Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, ChinaY.Y. Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, ChinaWe consider a nonlinear equation F(ε,λ,u)=0, where the parameter ε is a perturbation parameter, F is a differentiable mapping from R×R×X to Y, and X, Y are Banach spaces. We obtain an abstract bifurcation theorem by using the generalized saddle-node bifurcation theorem.http://dx.doi.org/10.1155/2011/302942
spellingShingle Ping Liu
Yuwen Wang
A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation
Abstract and Applied Analysis
title A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation
title_full A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation
title_fullStr A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation
title_full_unstemmed A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation
title_short A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation
title_sort fold bifurcation theorem of degenerate solutions in a perturbed nonlinear equation
url http://dx.doi.org/10.1155/2011/302942
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