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The Generalized Saddle-Node Bifurcation of Degenerate Solution

Ping Liu; Yu-Wen Wang — 2005

Commentationes Mathematicae

In this paper we discuss the bifurcation problem for the abstract operator equation of the form $F (u, λ) = θ$ with a parameter $λ$ , where $F : X \times R \to Y$ is a $C^{1}$ mapping, $X, Y$ are Banach spaces. By the bounded linear generalized inverse $A^{+}$ of $A = F_{u} (u_{0}, λ_{0})$ , an abstract bifurcation theorem for the case $dim N (F_{u} (u_{0}, λ_{0})) \geq codim R (F_{u} (u_{0}, λ_{0})) = 1$ has been obtained.

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