2019
Том 71
№ 10

# Martynyuk D. I.

Articles: 14
Article (Russian)

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

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 (Russian)

### Second bogolyubov theorem for systems of difference equations

Ukr. Mat. Zh. - 1996. - 48, № 4. - pp. 464-475

We establish an analog of the second Bogolyubov theorem for a system of difference equations.

Article (Ukrainian)

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

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

Article (Russian)

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

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

Sufficient conditions are established for the reducibility of a nonlinear system of difference equations $$x(x + 1) = x(1) + \omega + P(x(t), t) + \lambda,$$ where $P(x, t)$ is a function $2\pi$-periodic in $x_i(i = 1,..., n)$ and almost periodic in $t$ with a frequency basis $\alpha$, to the system $$y(t + 1) = y(t) + \omega.$$

Article (Russian)

### Reducibility of linear systems of difference equations with almost periodic coefficients

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

For the linear systemof difference equations $x(t + 1) = Ax(t) + P(t)x(t)$, where the matrix $P(t)$ is almost periodic, sufficient conditions are given, which reduce it to a system with a constant matrix.

Article (Ukrainian)

### Periodic solutions of nonlinear autonomous systems with delay

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

Article (Ukrainian)

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

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

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

Article (Ukrainian)

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

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

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

Article (Russian)

### Existence of invariant manifolds of systems with delay

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

Article (Ukrainian)

### N. P. Erugin. Book reviews

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

Article (Ukrainian)

### Periodic solutions of quasilinear autonomous systems with time-lag

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

Article (Ukrainian)

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

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