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.
@article{bwmeta1.element.doi-10_2478_BF02475963,
author = {Joanna Janczewska},
title = {Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {561-572},
zbl = {1078.47031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475963}
}
Joanna Janczewska. Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point. Open Mathematics, Tome 2 (2004) pp. 561-572. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475963/
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