Scientific articles

About the solvability of the Cauchy problem for nonlinear functional differential equations

T. V. Zhukovskaya^a, E. S. Zhukovskiy^bc, Kh. M. Takhir<sup>b

a</sup> Tambov State Technical University
^b Tambov State University named after G.R. Derzhavin
^c RUDN University

Abstract: 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, existence of solution.

UDC: 517.988.6, 517.922

Received: 17.04.2017

DOI: 10.20310/1810-0198-2017-22-3-523-532