The Generalized Saddle-Node Bifurcation of Degenerate Solution

• Autorzy: Ping Liu , Yu-Wen Wang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Operator equation; bifurcation; generalized inverse of operator

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2005
• Tom: 45
• Numer: 2

Daty

wydano

2005

online

2017-12-19

Twórcy

autor

Ping Liu

autor

Yu-Wen Wang

Identyfikatory

DOI

10.14708/cm.v45i2.5195