Source: wikibot/caratheodory-s-existence-theorem
= Carathéodory's existence theorem
{wiki=Carathéodory's_existence_theorem}
Carathéodory's existence theorem is a fundamental result in the theory of ordinary differential equations (ODEs). It provides conditions under which a first-order ordinary differential equation has at least one solution. The theorem is particularly important for equations that may not have Lipschitz continuity, allowing for broader applications.