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#carathéodory's_existence_theorem

Carathéodory's existence theorem

Statement on solutions to ordinary differential equations

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 be continuous, while Carathéodory's theorem shows existence of solutions for some discontinuous equations. The theorem is named after Constantin Carathéodory.

Fri 13th

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Carathéodory's existence theorem Carathéodory's theorem Picard–Lindelöf theorem Peano existence theorem Constantin Carathéodory Cauchy–Kovalevskaya theorem Ordinary differential equation Linear differential equation Frobenius theorem (differential topology) List of theorems

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