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New fixed point theorem and its application to ODE

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 Carathéodory's existence theorem.

preprint2023arXivOpen access
Oleg Zubelevich
math-phmath.MPmath.CA
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Oleg Zubelevich

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