On the existence, uniqueness, and asymptotics of the solution to the problem $F (t, x, x') = 0, x(0) = 0$

Zernov Oleksandr Evgeniovych; Kuzina  Yu. V.

Zernov Oleksandr Evgeniovych ¹ , Kuzina Yu. V. ²

¹ Department of Algebra and Geometry, South Ukrainian State Pedagogical University named after K. D. Ushynsky, Odesa, 65020, Ukraine

² Odessa Institute of Finance of the Ukrainian State University of Finance and International Trade, Odessa, 65070, Ukraine

Keywords: the existence, uniqueness, and asymptotics of the solution to the problem

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Abstract

The existence and uniqueness of a solution to the implicit Cauchy problem with the required asymptotic behavior is proved.

References

[1] Vityuk A. N. Generalized Cauchy problem for a system of differential equations not solved with respect to derivatives / / Differential equations. - 1971. - 7, N 9. - P. 1575-1580.

[2] Demidovich B. P. Lectures on the mathematical theory of stability. - M.: Nauka, 1967. - 472 p.

[3] Erugin N. P. A book for reading on the general course of differential equations. - Minsk: Science and Technology, 1972. - 664 p.

[4] Zernov A. E. Qualitative analysis of the implicit singular Cauchy problem// Ukrainian Mathematical Journal. - 2001. - 54, N 3. - P. 302-310.

[5] Nemytsky V. V. and Stepanov V. V. Qualitative theory of differential equations. - M.-L.: GITTL, 1949. - 550 p.

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[7] Conti R. Sulla risoluzione dell'equazione $F(t, x, {dx \over dt}) = 0$// Ann. mat. pura ed appl.- 1959.- N 48.— P.97-102.

[8] Kowalski Z. A difference method of solving the differential equation $y' = h(t, y, y, y')$ // Ann. polon. math. - 1965. — 15, N 2.— P.173-204.

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Cite

ACS Style: Zernov, O.E.; Kuzina , Y.V. On the existence, uniqueness, and asymptotics of the solution to the problem $F (t, x, x') = 0, x(0) = 0$. Bukovinian Mathematical Journal. 2018, 1
AMA Style: Zernov OE, Kuzina YV. On the existence, uniqueness, and asymptotics of the solution to the problem $F (t, x, x') = 0, x(0) = 0$. Bukovinian Mathematical Journal. 2018; 1(150).
Chicago/Turabian Style: Oleksandr Evgeniovych Zernov, Yu. V. Kuzina . 2018. "On the existence, uniqueness, and asymptotics of the solution to the problem $F (t, x, x') = 0, x(0) = 0$". Bukovinian Mathematical Journal. 1 no. 150.

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