J Austral Math Soc Ser A 43 pp246--256, 1987.

Uniqueness and Non-Uniqueness of Solutions of Vlasov-McKean Equations

Michael Scheutzow

(Received 5 March 1986; revised 29 September 1986)

Abstract

We study the equation dY(t)/dt = f(Y(t), Eh(Y(t))) for random initial conditions, where E denotes the expected value. It turns out that in contrast to the deterministic case local Lipschitz continuity of f and h are not sufficient to ensure uniqueness of the solutions. Finally we also state some sufficient conditions for uniqueness.

1980 AMS Subject Classification: 34F05, 35K22, 60H10 <\P>

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Authors

Michael Scheutzow: Fachbereich Mathematik, Universität Kaiserslauttern, D-6750 Kaiserslauttern, West Germany.

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Last Modified: Wed Feb 26 16:48:07 2003