2019
Том 71
№ 5

Yakovets V. P.

Articles: 10
Article (Ukrainian)

On the structure of the general solution and conditions of solvability of the Cauchy problem for degenerate linear systems of higher-order differential equations

Ukr. Mat. Zh. - 2013. - 65, № 2. - pp. 296-305

For a system of linear differential equations of order $p$ with identically degenerate coefficient matrix of the leading derivatives, we establish conditions under which it has a general solution of the Cauchy type. The structure of this solution is determined. Conditions for the existence and uniqueness of a solution of the corresponding initial-value problem are also found.

Anniversaries (Ukrainian)

Mykola Ivanovych Shkil' (on his 80th birthday)

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1720-1722

Article (Ukrainian)

Construction of Asymptotic Solutions of Linear Systems of Differential Equations with Two Small Parameters

Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 961-976

We consider a linear homogeneous system of differential equations with two small parameters. In this system, the dependence on one parameter is regular and on the other is singular. Using methods of the theory of perturbations of linear operators and a space analog of the Newton diagrams, we investigate the asymptotics of a general solution of this system in the case where its leading matrix has a multiple eigenvalue associated with a multiple elementary divisor.

Article (Ukrainian)

On Periodic Solutions of Degenerate Singularly Perturbed Linear Systems with Multiple Elementary Divisor

Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1403-1415

We establish sufficient conditions for the existence and uniqueness of a periodic solution of a system of linear differential equations with a small parameter and a degenerate matrix of coefficients of derivatives in the case of a multiple spectrum of a boundary matrix pencil. We construct asymptotics of this solution.

Article (Ukrainian)

On the structure of the general solution of a degenerate linear system of second-order differential equations

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 292–298

We establish sufficient conditions for the existence of a general Cauchy-type solution and conditions for the solvability of the Cauchy problem for a system of second-order differential equations.

Article (Ukrainian)

On some properties of degenerate linear systems

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1278–1296

Для лінійної системи звичайних диференціальних рівнянь з виродженою матрицею при похідних знайдено умови звідності до центральної канонічної форми, встановлено структуру загального розв'язку та умови розв'язності задачі Коші, досліджено питання про періодичні розв'язки.

Article (Ukrainian)

Asymptotics of the general solution to a linear singularly perturbed system of second-order differential equations with degeneracy

Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 561–575

By using the perturbation methods and Newton diagrams, we study the structure and construct the asymptotics of the general solution to a linear singularly perturbed system of ordinary second-order differential equations in the case where the matrix by the higher derivative is degenerate.

Article (Ukrainian)

Construction of asymptotic solutions of linear singularly perturbed systems of second order with degeneracy

Ukr. Mat. Zh. - 1992. - 44, № 8. - pp. 1102–1112

Article (Ukrainian)

Asymptotic convergence of formal solutions of linear systems of differential equations with slowly varying coefficients

Ukr. Mat. Zh. - 1987. - 39, № 6. - pp. 802-807

Article (Ukrainian)

Asymptotic integration of certain systems of linear partial differential equations

Ukr. Mat. Zh. - 1983. - 35, № 2. - pp. 187—193