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The Generalized Saddle-Node Bifurcation of Degenerate Solution

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Liu P., Wang Y.-W.

Commentationes Mathematicae

2005

tom 45

nr 2

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.

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1 Commentationes Mathematicae

1 Liu P.

1 Wang Y.-W.

1 2005

Wyniki wyszukiwania

The Generalized Saddle-Node Bifurcation of Degenerate Solution