Carathéodory's Existence Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.