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math.CA2023
New fixed point theorem and its application to ODE
Oleg Zubelevich
We prove a fixed point theorem that combines the contraction mapping principle and some Knaster-Tarski-like theorem. As a consequence we obtain an existence theorem to initial valu…
math.CA2022
Monotone ODEs with Discontinuous Vector Fields in Sequence Spaces
Oleg Zubelevich
We consider a system of ODE in a Fréchet space with unconditional Schauder basis. The right side of the ODE is a discontinuous function. Under certain monotonicity conditions we pr…
math.CA2020
Forward-Backward Bounded Solutions to Differential Inclusions
Oleg Zubelevich
It is shown that some class of differential inclusions has solutions that are defined and bounded for all real values of independent variable. Applications to dynamics are consider…