2019
Том 71
№ 11

# Teplinsky Yu. V.

Articles: 20
Article (Ukrainian)

### Truncation method for countable-point boundary-value problems in the space of bounded number sequences

Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1203-1230

We consider possible methods for the reduction of a countable-point nonlinear boundary-value problem with nonlinear boundary condition on a segment to a finite-dimensional multipoint problem constructed on the basis of the original problem by the truncation method. The results obtained are illustrated by examples.

Article (Ukrainian)

### On the Cauchy Problem for Degenerate Difference Equations of the mth Order in a Banach Space

Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1127-1137

We establish sufficient conditions for the solvability of the Cauchy problem for degenerate difference equations of the mth order in a Banach space.

Article (Ukrainian)

### On the Fréchet Differentiability of Invariant Tori of Countable Systems of Difference Equations Defined on Infinite-Dimensional Tori

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 75-90

By using the method of Green–Samoilenko functions, in the space of bounded number sequences we construct invariant tori of linear and nonlinear systems of discrete equations defined on infinite-dimensional tori. We establish sufficient conditions for the Fréchet differentiability of invariant tori.

Article (Ukrainian)

### International Scientific Conference on the Theory of Evolution Equations (Fifth Bogolyubov Readings)

Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1440

Article (Ukrainian)

### On the Smoothness of the Invariant Torus of a Countable System of Difference Equations with Parameters

Ukr. Mat. Zh. - 2001. - 53, № 9. - pp. 1241-1250

We establish sufficient conditions for the differentiability of the invariant torus of a countable system of linear difference equations defined on a finite-dimensional torus with respect to an angular variable and the parameter of the original system of equations.

Article (Russian)

### Limit theorems in the theory of multipoint boundary-value problems

Ukr. Mat. Zh. - 1999. - 51, № 4. - pp. 519–531

We present a reduction of a countable system of differential equations with countably-point boundary conditions to the case of a finite-dimensional multipoint boundary-value problem. We separately consider the case of a linear system.

Article (Russian)

### Invariant tori of linear countable systems of discrete equations given on an infinite-dimensional torus

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 244–251

We study the problem of existence and uniqueness of invariant toroidal manifolds of countable systems of linear equations given on an infinite-dimensional torus.

Chronicles (Ukrainian)

### Ukrainian school-seminar "Nonlinear boundary value problems of mathematical physics and applications"

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 613–617

Article (Russian)

### On periodic solutions of countable systems of linear and quasilinear difference equations with periodic coefficients

Ukr. Mat. Zh. - 1996. - 48, № 8. - pp. 1144-1152

We present conditions for the existence of periodic solutions of linear difference equations with periodic coefficients in spaces of bounded number sequences. In the case where the generating linear equation has a unique periodic solution, we indicate sufficient conditions for the existence of a periodic solution of a quasilinear difference equation.

Article (Russian)

### On the erugin and floquet-lyapunov theorems for countable systems of difference equations

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 278-284

For linear difference equations in the space of bounded number sequences, we prove an analog of the Erugin theorem on reducibility and present sufficient conditions for the reducibility of countable linear systems of difference equations with periodic coefficients.

Article (Russian)

### On the reducibility of countable systems of linear difference equations

Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1533–1541

We solve the problem of reducibility of a countable linear system of standard difference equations with unbounded right-hand sides by the method of construction of iterations with accelerated convergence. For systems of this type with bounded right-hand sides, this problem is reduced to a finite-dimensional case.

Article (Russian)

### Dependence of Green’s function of an $e$-dichotomous differential equation with matrix projector in the space M on parameters

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 748–753

In the space $\mathfrak{M}$ of bounded numeric sequences, we consider dichotomonly differential equation with a matrix projector. We prove that Green's function of this equation exists, and give the conditions, under which it is continuous and differentiable with respect to the parameters in the equation.

Article (Russian)

### On decomposability of countable systems of differential equations

Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1424–1432

Conditions under which there exists a change of variables that decomposes a countable system of differential equations are established for the entire real axis and a semiaxis. Similar problems are investigated for a countable system with pulse influence.

Article (Ukrainian)

### Reduction of a problem on the existence of an invariant torus of an infinite-differential system to the finite-dimensional case

Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1251–1255

Article (Ukrainian)

### The reducibility of differential equations with impulses in the space of bounded numerical sequences

Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1376–1382

Article (Ukrainian)

### Exponential stability of an invariant torus of a nonlinear countable system of differential equations

Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 401–405

Article (Ukrainian)

### A certain periodic control problem for differential equations with impulses in the space of bounded numerical sequences

Ukr. Mat. Zh. - 1990. - 42, № 2. - pp. 271–275

Article (Ukrainian)

### Invariant tori of linear systems of differential equations in the space m

Ukr. Mat. Zh. - 1983. - 35, № 2. - pp. 194—199

Article (Ukrainian)

### Question of reductibility of countable systems of differential equations with quasiperiodic coefficients

Ukr. Mat. Zh. - 1979. - 31, № 4. - pp. 463–465

Article (Ukrainian)

### The existence of the invariant toroidal manifold of a countable system of differential equations with impulsive action

Ukr. Mat. Zh. - 1977. - 29, № 6. - pp. 835–841