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The existence and estimates of solutions of the Cauchy problem or a nonlinear functional-differential equation

Annotation

We obtain an assertion about functional-differential inequality analogous to the well-known theorem of Chaplygin. The result can be used to find estimates of solutions of specific functional-differential equations.

Keywords

Cauchy problem; functional-differential equation; the Chaplygin theorem on differential inequality

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DOI

10.20310/1810-0198-2017-22-6-1329-1334

UDC

517

Pages

1329-1334

References

1. Krasnoselsky M.A., Zabreiko P.P. Geometricheskie metody nelinejnogo analiza. M: Nauka, 1975. 512 p. 2. Azbelev N.V., Maksimov V.P., Rahmatullina L.F. Vvedenie v teoriyu funkcionalno-differencialnyh uravnenij. M: Nauka, 1991. 280 s. 3. Kantorovich L.V. Akilov G.P Funkcionalnyj analiz. M: Nauka, 1984. 752 s. 4. Zhukovskij E.S. Contribution to the theory of Volterra equations // Differential Equations. 1989. V. 25. Iss. 9. P. 1132–1137. 5. Maksimov V.P. The Cauchy formula for a functional-differential equation // Differential Equations. 1977. V. 13. Iss. 4. P. 601–606.

Received

2017-08-03

Section of issue

Mathematics

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