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

Joanna Janczewska

Open Mathematics (2004)

  • Volume: 2, Issue: 4, page 561-572
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Joanna Janczewska. "Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point." Open Mathematics 2.4 (2004): 561-572. <http://eudml.org/doc/268857>.

@article{JoannaJanczewska2004,
abstract = {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.},
author = {Joanna Janczewska},
journal = {Open Mathematics},
keywords = {34K18},
language = {eng},
number = {4},
pages = {561-572},
title = {Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point},
url = {http://eudml.org/doc/268857},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Joanna Janczewska
TI - Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point
JO - Open Mathematics
PY - 2004
VL - 2
IS - 4
SP - 561
EP - 572
AB - 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.
LA - eng
KW - 34K18
UR - http://eudml.org/doc/268857
ER -

References

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