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1
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Bounded solutions to a system of second order ODEs and the Whitney pendulum

100%
Zubelevich O.
Applicationes Mathematicae
|
2015
|
tom 42
|
nr 2-3
159-165
EN
We give an existence theorem for bounded solutions to a system of second order ODEs. Dynamical applications are considered.
2
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A fixed point theorem for affine mappings and its application to elasticity theory

100%
Zubelevich O.
Open Mathematics
|
2010
|
tom 8
|
nr 6
1104-1108
EN
In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.
3
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Evolution differential equations in Fréchet sequence spaces

100%
Zubelevich O.
Colloquium Mathematicum
|
2016
|
tom 143
|
nr 2
251-264
EN
We consider evolution differential equations in Fréchet spaces with unconditional Schauder basis, and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE are also considered.
4
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Abstract version of the Cauchy-Kowalewski problem

100%
Zubelevich O.
Open Mathematics
|
2004
|
tom 2
|
nr 3
382-387
EN
We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem.
5
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On weak solutions to the Lagrange-d'Alembert equation

64%
Treschev D., Zubelevich O.
Applicationes Mathematicae
|
2013
|
tom 40
|
nr 3
383-392
EN
We consider nonholonomic systems with collisions and propose a concept of weak solutions to Lagrange-d'Alembert equations. Using this concept we describe the dynamics of collisions. Collisions of a rotating ball and a rough floor are considered.
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