Open AccessA Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation
Author(s) -
Ping Liu,
Yuwen Wang
Publication year - 2011
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2011/302942
Subject(s) - mathematics , bifurcation , differentiable function , banach space , saddle node bifurcation , mathematical analysis , perturbation (astronomy) , bifurcation theory , degenerate energy levels , nonlinear system , pure mathematics , physics , quantum mechanics
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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