About: Carathéodory's existence theorem

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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 (in a more general sense) for some discontinuous equations. The theorem is named after Constantin Carathéodory.

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rdfs:label	Carathéodory's existence theorem (en)
rdfs:comment	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 (in a more general sense) for some discontinuous equations. The theorem is named after Constantin Carathéodory. (en)
sameAs	Carathéodory's existence theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Portal dbt:Short_description dbt:Differential_equations
Subject	Theorems in analysis Ordinary differential equations
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Carathéodory's_existence_theorem?oldid=993657825&ns=0
Wikipage page ID	21075081 (xsd:integer)
page length (characters) of wiki page	6315 (xsd:nonNegativeInteger)
Wikipage revision ID	993657825 (xsd:integer)
Link from a Wikipage to another Wikipage	Absolute continuity Almost everywhere Theorems in analysis Cauchy–Kowalevski theorem Ordinary differential equations Picard–Lindelöf theorem Constantin Carathéodory Continuous function Ordinary differential equation Heaviside step function Peano existence theorem Lebesgue integration Mathematics McGraw Hill Education Measurable function Ramp function dbr:Robert_E._Krieger_Publishing_Company
has abstract	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 (in a more general sense) for some discontinuous equations. The theorem is named after Constantin Carathéodory. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Carathéodory's_existence_theorem
is Wikipage redirect of	Caratheodory's existence theorem Carathéodory existence theorem
is Link from a Wikipage to another Wikipage of	List of theorems Caratheodory's existence theorem Caratheodory-π solution Carathéodory's theorem Linear differential equation List of dynamical systems and differential equations topics Constantin Carathéodory Federico Cafiero Initial value problem Carathéodory existence theorem
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Carathéodory's_existence_theorem

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