Lidé

Paola Vivi, Ph.D.

Všechny publikace

Cross-sections of solution funnels

  • DOI: 10.1016/j.jmaa.2015.08.026
  • Odkaz: https://doi.org/10.1016/j.jmaa.2015.08.026
  • Pracoviště: Katedra matematiky
  • 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
  • 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

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
  • 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.

Za stránku zodpovídá: Ing. Mgr. Radovan Suk