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New fixed point theorem and its application to ODE (2301.04437v2)
Published 11 Jan 2023 in math.CA, math-ph, and 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.
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