2 citations · 2 across the 24 of their papers we have counts for
25 papers
The D'Alembert-Lagrange Principle and Lagrange Equations
Oleg Zubelevich
This expository article serves as a methodical guide, presenting a rigorous mathematical formulation of the D'Alembert-Lagrange principle and the derivation of the Lagrange equatio…
A Note on Brondsted's Fixed Point Theorem
Oleg Zubelevich
We show that for the case of uniformly convex Banach spaces the conditions of the Brondsted fixed point theorem can be relaxed.
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…
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…
The Lagrange-D'Alembert Principle in Banach Space
Oleg Zubelevich
The Lagrange-D'Alembert Principle is one of the fundamental tools of classical mechanics. We generalize this principle to mechanics-like ODE in Banach spaces. As an application we…
The Lagrange-D'Alembert Principle from the Viewpoint of ODE
Oleg Zubelevich
We formulate the Lagrange-D'Alembert principle as a pure mathematical theory that meets modern standards of rigor. While we note several new aspects of the principle, the article i…