Geodesic
The existence of solutions of generalized differential equations
Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 307-313

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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. 
@article{MZM_1971_10_3_a8,
     author = {A. F. Filippov},
     title = {The existence of solutions of generalized differential equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {307--313},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a8/}
}
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A. F. Filippov. The existence of solutions of generalized differential equations. Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 307-313. http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a8/