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Bifurcation at Double Characteristic Values
Author(s) -
Westreich David
Publication year - 1977
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-15.2.345
Subject(s) - bifurcation , mathematics , homogeneous , degenerate energy levels , operator (biology) , bifurcation theory , sign (mathematics) , constructive , mathematical analysis , saddle node bifurcation , transcritical bifurcation , nonlinear system , computer science , combinatorics , physics , process (computing) , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , operating system
The double characteristic value bifurcation problem is considered where the leading non‐linear term is a homogeneous operator. The problem is reduced to that of examining a functional of the homogeneous operator. Bifurcation is shown to occur when the functional changes sign. If the functional is non‐degenerate at an eigenray then there exists a bifurcating solution branch depending on a real parameter and a constructive method of obtaining these solutions is given.