Geodesic
About the solvability of the Cauchy problem for nonlinear functional differential equations
Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 3, pp. 523-532

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The Cauchy problem for a nonlinear functional-differential equation of general type with Volterra mappings is considered. Conditions of existence of a unique global solution and conditions of existence of a unique limitary prolonged solution are derived. The reduction to an operator equation with the Volterra operator in the space of continuous functions is used.
Keywords: the Volterra operator, nonlinear functional-differential equation, the Cauchy problem
Mots-clés : existence of solution. 
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     author = {T. V. Zhukovskaya and E. S. Zhukovskiy and Kh. M. Takhir},
     title = {About the solvability of the {Cauchy} problem for nonlinear functional differential equations},
     journal = {Vestnik rossijskih universitetov. Matematika},
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     publisher = {mathdoc},
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     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2017_22_3_a3/}
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T. V. Zhukovskaya; E. S. Zhukovskiy; Kh. M. Takhir. About the solvability of the Cauchy problem for nonlinear functional differential equations. Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 3, pp. 523-532. http://geodesic.mathdoc.fr/item/VTAMU_2017_22_3_a3/