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A generalization of Carathéodory's existence theorem for ordinary differential equations

✍ Scribed by Jan Persson

Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
369 KB
Volume
49
Category
Article
ISSN
0022-247X

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📜 SIMILAR VOLUMES

On Generalized Carathéodory's Conditions
On Generalized Carathéodory's Conditions in Ordinary Differential Equations
✍ Dariusz Bugajewski; Daria Wójtowicz 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 212 KB

In this paper we prove that generalized Carathbdory's conditions (so called (G) ronditions) imply wellknown general conditions which guarantee existence and some properties of Nolutions of the Cauchy problem, in the Carathhdory sense, .B e. g. continuous dependence on initial ronditions.

A generalization of carathéodory's theor
A generalization of carathéodory's theorem
✍ Imre Bárány 📂 Article 📅 1982 🏛 Elsevier Science 🌐 English ⚖ 812 KB

The following theorem is lproved. If the sets VI, . . . , Vn+, CR" and a E fly:: conv Vi, then there exist elements ui E Vi (i = 1, . . . , n + 1) such that a E conv{o,, . . . , un+J. Thii is a generalization of Carathtidory's theorem. By applying this and similar results some open questions are ans