2019
Том 71
№ 2

All Issues

Teplinsky Yu. V.

Articles: 19
Article (Ukrainian)

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

Nedokis V. A., Samoilenko A. M., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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

Semenyshyna I. V., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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

Marchuk N. A., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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)

Konet I. M., Perestyuk N. A., Samoilenko A. M., Teplinsky Yu. V.

Full text (.pdf)

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

Marchuk N. A., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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

Nedokis V. A., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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

Samoilenko A. M., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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"

Berezovsky A. A., Konet I. M., Lenyuk M. P., Samoilenko A. M., Teplinsky Yu. V.

Full text (.pdf)

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

Samoilenko M. V., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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

Teplinsky Yu. V., Teplins’kyi O. Yu.

↓ Abstract   |   Full text (.pdf)

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 (Ukrainian)

Dependence of Green?s function of an e-dichotomous differential equation with matrix projector in the space $\mathfrak{M}$ on parameters

Teplinsky Yu. V.

Full text (.pdf)

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

Article (Ukrainian)

On decomposability of countable systems of differential equations

Samoilenko A. M., Teplinsky Yu. V.

↓ Abstract   |   Full text (.pdf)

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

Avdeyuk P. I., Teplinsky Yu. V.

Full text (.pdf)

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

Luchik V. E., Teplinsky Yu. V.

Full text (.pdf)

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

Avdeyuk P. I., Teplinsky Yu. V.

Full text (.pdf)

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

Teplinsky Yu. V., Tsyganovsky N. S.

Full text (.pdf)

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

Article (Ukrainian)

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

Teplinsky Yu. V.

Full text (.pdf)

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

Article (Ukrainian)

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

Teplinsky Yu. V.

Full text (.pdf)

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

Teplinsky Yu. V.

Full text (.pdf)

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