On Carathéodoryʼs Conditions Revisited

Dariusz Bugajewski

doi:rae/1230995423

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Home > Journals > Real Anal. Exchange > Volume 25 > Issue 2 > Article

1999/2000 On Carathéodoryʼs Conditions Revisited

Dariusz Bugajewski

Real Anal. Exchange 25(2): 899-906 (1999/2000).

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Abstract

In [3] we proved that generalized Carathéodory's conditions (the so called (G) conditions) introduced in [6], imply well-known general conditions (the so called (CL) conditions) which guarantee existence and some properties of solutions of the Cauchy problem, in the Carathéodory sense. In this paper we prove that these two conditions are equivalent.