2018
Том 70
№ 7

All Issues

Martynyuk D. I.

Articles: 13
Article (Russian)

Periodic solutions of systems of differential equations with random right-hand sides

Danilov V. Ya., Martynyuk D. I., Stanzhitskii A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 223–227

We prove a theorem on the existence of periodic solutions of a system of differential equations with random right-hand sides and small parameter of the form dx/dt=εX(t, x, ξ(t)) in a neighborhood of the equilibrium state of the averaged deterministic system dx/dtX 0(t).

Article (Ukrainian)

Reducibility of nonlinear almost periodic systems of difference equations on an infinite-dimensional torus

Martynyuk D. I., Perestyuk N. A., Samoilenko A. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1216–1223

Article (Ukrainian)

Reducibility of nonlinear almost periodic systems of difference equations given on a torus

Martynyuk D. I., Perestyuk N. A., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 404–412

We establish sufficient conditions for a nonlinear system of difference equations x(t + 1) =x(t) + ? + P(x(t),t)+ ? to be reducible to the system y(t + 1) =y(t) + ?. Here, P(x, t) is a function 2?-periodic in xi(i = 1, ...,n) and almost periodic int with a frequency basis ?.

Article (Ukrainian)

Reducibility of linear systems of difference equations with almost periodic coefficients

Martynyuk D. I., Mitropolskiy Yu. A., Tynnyi V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1661–1667

We establish sufficient conditions of the reducibility of the linear system of difference equationsx(t+1)=Ax(t) + P(t) x(t) with an almost periodic matrixP(t) to a system with a constant matrix.

Article (Ukrainian)

Periodic solutions of nonlinear autonomous systems with delay

Martynjuk, Martynyuk D. I.

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Ukr. Mat. Zh. - 1987. - 39, № 1. - pp. 64–68

Article (Ukrainian)

A control problem for systems, of second-order differential equations with retarded argument

Martynyuk D. I., Mitropolskiy Yu. A., Yurchik A. I.

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Ukr. Mat. Zh. - 1985. - 37, № 5. - pp. 594–599

Article (Ukrainian)

Solution of a control problem for systems with delay by the method of two-sided approximations

Martynyuk D. I., Mitropolskiy Yu. A., Yurchik A. I.

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Ukr. Mat. Zh. - 1985. - 37, № 4. - pp. 462–467

Article (Ukrainian)

Oscillatory modes of weakly linear systems with n degrees of freedom and delay

Kravets V. I., Martynyuk D. I.

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Ukr. Mat. Zh. - 1984. - 36, № 1. - pp. 115 - 118

Article (Ukrainian)

Galerkin's method in the theory of quasiperiodic solutions of nonlinear differential equations with lag

Martynjuk, Martynyuk D. I., Mitropolskiy Yu. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 4. - pp. 553–557

Article (Russian)

Existence of invariant manifolds of systems with delay

Martynyuk D. I., Samoilenko A. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1974. - 26, № 5. - pp. 611–620

Article (Ukrainian)

N. P. Erugin. Book reviews

Bondarenko P. S., Martynyuk D. I., Pavlyuk I. A., ShkiI N. I., Shtokalo I. Z.

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Ukr. Mat. Zh. - 1970. - 22, № 6. - pp. 848—851

Article (Ukrainian)

Periodic solutions of quasilinear autonomous systems with time-lag

Kozubovskaya I. G., Martynyuk D. I.

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Ukr. Mat. Zh. - 1968. - 20, № 2. - pp. 263–265

Article (Ukrainian)

Periodical solutions of nonlinear differential equations of second order with a Lagging argument

Martynyuk D. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1967. - 19, № 4. - pp. 125–132