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

Open Mathematics (2004)

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

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topJoanna 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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