Open AccessA degenerate bifurcation from simple eigenvalue theorem
Author(s) -
Ping Liu,
AUTHOR_ID,
Junping Shi,
AUTHOR_ID
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022006
Subject(s) - mathematics , bifurcation , degenerate energy levels , eigenvalues and eigenvectors , bifurcation theory , mathematical analysis , simple (philosophy) , tangent , saddle node bifurcation , transcritical bifurcation , transversal (combinatorics) , line (geometry) , nonlinear system , geometry , physics , philosophy , epistemology , quantum mechanics
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.