Lidé
Paola Vivi, Ph.D.
Všechny publikace
Cross-sections of solution funnels
- Autoři: prof. Mgr. Petr Hájek, DrSc., Paola Vivi, Ph.D.,
- Publikace: Journal of Mathematical Analysis and Applications. 2016, 433(2), 957-973. ISSN 0022-247X.
- Rok: 2016
- DOI: 10.1016/j.jmaa.2015.08.026
- Odkaz: https://doi.org/10.1016/j.jmaa.2015.08.026
- Pracoviště: Katedra matematiky
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Anotace:
Let X be a separable infinite dimensional real Banach space. We denote by F(X)F(X) the class of continuous functions f:R×X→Xf:R×X→X such that the ODE View the MathML sourceu′=f(t,u),u(t0)=x,t0∈R,x∈X, has a global solution for any initial condition. Our main result states that A⊂XA⊂X is the cross-section of a solution funnel of the ODE u′=f(t,u),u(0)=0u′=f(t,u),u(0)=0, for some f∈F(X)f∈F(X), if and only if A is an analytic set.
On \omega Limit Sets of Ordinary Differential Equations in Banach Spaces
- Autoři: Hajek, P., Paola Vivi, Ph.D.,
- Publikace: Journal of Mathematical Analysis and Its Applications. 2010, 371(2), 793-812. ISSN 0022-247X.
- Rok: 2010
- DOI: 10.1016/j.jmaa.2010.05.059
- Odkaz: https://doi.org/10.1016/j.jmaa.2010.05.059
- Pracoviště: Katedra matematiky
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Anotace:
Let X be an infinite-dimensional real Banach space. We classify omega-limit sets of autonomous ordinary differential equations x' = f(x), x(0) = x(0), where f : X -> X is Lipschitz, as being of three types I-III.
Some Problems on Ordinary Differential Equations in Banach Spaces
- Autoři: Hajek, P., Paola Vivi, Ph.D.,
- Publikace: Revista de la Real Academia de Ciencias. 2010, 104(2), 245-255. ISSN 1578-7303.
- Rok: 2010
- DOI: 10.5052/RACSAM.2010.16
- Odkaz: https://doi.org/10.5052/RACSAM.2010.16
- Pracoviště: Katedra matematiky
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Anotace:
We survey some results on ordinary differential equations in Banach spaces and pose several related open problems
Hopf bifurcations of functional differential equations with dihedral symmetries
- Autoři: Paola Vivi, Ph.D., Krawcewicz, W.
- Publikace: JOURNAL OF DIFFERENTIAL EQUATIONS. 1998, 146(1), 157-184. ISSN 0022-0396.
- Rok: 1998
- DOI: 10.1006/jdeq.1998.3422
- Odkaz: https://doi.org/10.1006/jdeq.1998.3422
- Pracoviště: Katedra matematiky
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Anotace:
We discuss the joint impact of temporal delay and spatial dihedral symmetries on the occurence and multiplicity of Hopf bifurcations for a system of FDEs. By applying the equivariant degree theory we establish a result on the existence of multiple branches of nonconstant periodic solutions and classify their symmetries. General results are illustrated by a ring of identical oscillators with identical coupling between adjacent cells. (C) 1998 Academic Press.