In mathematics, **Carathéodory's existence theorem** says that an ordinary differential equation has a solution under relatively mild conditions. It is a generalization of Peano's existence theorem. Peano's theorem requires that the right-hand side of the differential equation is continuous, while Carathéodory's theorem shows existence of solutions (in a more general sense) for some discontinuous equations. The theorem is named after Constantin Carathéodory.

Read more about Carathéodory's Existence Theorem: Introduction, Statement of The Theorem

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