Geodesic
Cauchy problem for nonlinear functional-differential equation
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 36 (2006) no. 2, pp. 53-56.

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We offer confirmations about solveness and persistent dependentness from initial conditions of functional-differential equations with operator of volterra according to A. N. Tihonov, which acts in arbitrary Banah spaces. With proper chose of spaces those results can be used to investigate not only classical functional-differential equations, but singular, impulsive, hybrid systems and so on. 
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E. S. Zhukovskiy. Cauchy  problem for nonlinear functional-differential equation. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 36 (2006) no. 2, pp. 53-56. http://geodesic.mathdoc.fr/item/IIMI_2006_36_2_a11/

[1] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Elementy sovremennoi teorii funktsionalno-differentsialnykh uravnenii. Metody i prilozheniya, Institut kompyuternykh issledovanii, M., 2002, 384 pp.

[2] Zhukovskii E. S., “Nelineinoe uravnenie Volterra v banakhovom funktsionalnom prostranstve”, Izv. vuzov. Matematika, 2005, no. 10 (521), 17–28 | MR