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ABOUT THE SOLVABILITY OF THE CAUCHY PROBLEM FOR NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

Annotation

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

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DOI

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

UDC

517.988.6, 517.922

Pages

523-532

References

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Received

2017-04-17

Section of issue

Functional-differential equations and inclusions and their applications to mathematical modeling

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