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On Generalized Carathéodory's Conditions in Ordinary Differential Equations

✍ Scribed by Dariusz Bugajewski; Daria Wójtowicz

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
212 KB
Volume
199
Category
Article
ISSN
0025-584X

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✦ Synopsis

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.

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✍ Antonios Zagaris; Hans G. Kaper; Tasso J. Kaper 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 169 KB

## Abstract This article is concerned with general nonlinear evolution equations __x__ ′ = __g__ (__x__ ) in **R**^__N__^ involving multiple time scales, where fast dynamics take the orbits close to an invariant low‐dimensional manifold and slow dynamics take over as the state approaches the manif