Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point

• Autorzy: Joanna Janczewska
• Języki publikacji: EN

Abstrakty

EN

In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R k →Y is a C 2-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R 1 that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ0)∈X×R k and we describe the solution set of the studied equation in a small neighbourhood of this point.

Słowa kluczowe

EN

bifurcation; finite-dimensional reduction; Fredholm operator; implicit function; variational gradient; 34K18

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 4
• Strony: 561-572

Daty

wydano

2004-08-01

online

2004-08-01

Twórcy

autor

Joanna Janczewska

• Gdańsk University of Technology

Bibliografia

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Identyfikatory

DOI

10.2478/BF02475963