High Quality Content by WIKIPEDIA articles! In mathematics, Caratheodory'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 Caratheodory's theorem shows existence of solutions (in a more general sense) for some discontinuous equations. The theorem is named after Constantin Caratheodory.

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