Geodesic
Nagumo theorem for systems with aftereffect
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 25 (2002) no. 2, pp. 11-14.

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Analogue of theorem Nagumo about viability for Banach space is established. Concrete example is considered. 
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V. N. Baranov. Nagumo theorem for systems with aftereffect. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 25 (2002) no. 2, pp. 11-14. http://geodesic.mathdoc.fr/item/IIMI_2002_25_2_a1/

[1] Aubin J.-P., Viability theory, Birkhauser, Boston, 1991, 326 pp. | MR | Zbl

[2] Tonkov E. L., “Dinamicheskie zadachi vyzhivaniya”, Vestn. Perm. gos. tekh. un-ta. Funktsion.-differents. uravneniya, 1997, no. 4, spets. vyp., 138–148