This article is cited in 40 papers

The existence of solutions of generalized differential equations

A. F. Filippov

M. V. Lomonosov Moscow State University

Abstract: The existence is proved of a solution of the equation $\dot{x}\in F(t,x)$, where $F(t,x)$ is a nonempty closed set depending continuously on $t$ and $x$, with no assumptions concerning the convexity of this set.

UDC: 517.91/4

Received: 02.10.1970

 English version: Mathematical Notes, 1971, 10:3, 608–611

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