2019
Том 71
№ 2

All Issues

Terekhin M. T.

Articles: 6
Article (Russian)

Existence of Small Periodic Solutions of Nonlinear Systems of Ordinary Differential Equations

Terekhin M. T.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 5. - pp. 680-687

We investigate the case where conditions for the existence of a nonzero periodic solution of a system of ordinary differential equations are determined by the properties of elements of the matrix of linear approximation and the properties of nonlinear terms.

Article (Russian)

The existence of a bifurcation value of a parameter of a system of differential equations with deviating argument

Nasykhova L. V., Terekhin M. T.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 6. - pp. 799–805

We prove a theorem on the existence of a nonzero periodic solution of a system of differential equations with deviation that depends both on an unknown function and on its derivative. This result is obtained for the case where the matrix of linear approximation has zero and imaginary eigenvalues if the parameter takes a critical value.

Article (Ukrainian)

Nontrivial periodic solutions of a nonautonomous system of second-order differential equations

Terekhin M. T.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 754–759

We prove theorem, in which basic conditions for the existence of nontrivial periodic solutions are formulated in terms of the properties of the elements of the matrix of a linear approximation to a system.

Article (Ukrainian)

Existence of a nonzero periodic solution of a singularly perturbed system of ordinary differential equations

Terekhin M. T., Vansovich M. O.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1318–1322

Article (Ukrainian)

Bifurcation of a periodic solution of a system of ordinary differential equations

Terekhin M. T.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 390–393

Article (Ukrainian)

Bifurcations of systems of ordinary differential equations

Terekhin M. T.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 5. - pp. 666–669