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Research Article | Open Access

A degenerate bifurcation from simple eigenvalue theorem

Ping Liu1, Junping Shi2( )
Y. Y. Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, China
Department of Mathematics, William & Mary, Williamsburg, VA 23187-8795, USA
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Abstract

A new bifurcation from simple eigenvalue theorem is proved for general nonlinear functional equations. It is shown that in this bifurcation scenario, the bifurcating solutions are on a curve which is tangent to the line of trivial solutions, while in typical bifurcations the curve of bifurcating solutions is transversal to the line of trivial ones. The stability of bifurcating solutions can be determined, and examples from partial differential equations are shown to demonstrate such bifurcations.

Keywords

degenerate bifurcationsimple eigenvaluetangential bifurcation

References

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Electronic Research Archive
Volume 30 Issue 1,
January 2022
Pages 116-125
DOI: 10.3934/era.2022006

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Cite this article:
Liu P, Shi J. A degenerate bifurcation from simple eigenvalue theorem. Electronic Research Archive, 2022, 30(1): 116-125. https://doi.org/10.3934/era.2022006

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Received: 26 August 2021
Revised: 16 November 2021
Accepted: 16 November 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)