Geodesic
The Generalized Saddle-Node Bifurcation of Degenerate Solution
Commentationes Mathematicae, Tome 45 (2005) no. 2, pp. 145-150 Cet article a éte moissonné depuis la source Annales Societatis Mathematicae Polonae Series

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In this paper we discuss the bifurcation problem for the abstract operator equation of the form \(F (u, \lambda) = \theta\) with a parameter \(\lambda\), where \(F\colon X \times R \to Y\) is a \(C^1\) mapping, \(X, Y\) are Banach spaces. By the bounded linear generalized inverse \(A^+\) of \(A = F_u (u_0 , \lambda_0 )\), an abstract bifurcation theorem for the case \(\operatorname{dim}N (F_u (u_0 , \lambda_0 )) \geq \operatorname{codim} R(F_u (u_0 , \lambda_0 )) = 1\) has been obtained.
DOI : 10.14708/cm.v45i2.5195
Mots-clés : Operator equation, bifurcation, generalized inverse of operator 
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Ping Liu; Yu-Wen Wang. The Generalized Saddle-Node Bifurcation of Degenerate Solution. Commentationes Mathematicae, Tome 45 (2005) no. 2, pp.  145-150. doi: 10.14708/cm.v45i2.5195

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