New fixed point theorem and its application to ODE
Classical Analysis and ODEs
2023-01-18 v2 Mathematical Physics
math.MP
Abstract
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 value problem for ordinary differential equation with discontinuous vector field. This theorem generalizes Carath\'eodory's existence theorem.
Cite
@article{arxiv.2301.04437,
title = {New fixed point theorem and its application to ODE},
author = {Oleg Zubelevich},
journal= {arXiv preprint arXiv:2301.04437},
year = {2023}
}
Comments
the paper contains a fatal error