2019
Том 71
№ 9

All Issues

Akhmetov M. U.

Articles: 11
Article (Ukrainian)

Rank criteria for the controllability of a boundary-value problem for a linear system of integro-differential equations with pulse influence

Akhmetov M. U., Seilova R. D.

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Ukr. Mat. Zh. - 2000. - 52, № 6. - pp. 723–730

We determine necessary and sufficient conditions for the solvability of boundary-value problems for a linear system of integro-differential equations with pulse influence. We prove theorems on the existence and integral representation of solutions of linear second order integral-sum Volterra equations and linear systems of integro-differential equations with pulse influence at fixed times.

Article (Russian)

Control over linear pulse systems

Akhmetov M. U., Perestyuk N. A., Tleubergenov M. I.

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Ukr. Mat. Zh. - 1995. - 47, № 3. - pp. 307–314

Rank conditions for control of linear pulse systems are established. The Pontryagin maximum principle is obtained in sufficient form. An example of control synthesis in a problem for linear pulse systems is given.

Article (Ukrainian)

On the smoothness of solutions of differential equations with a discontinuous right-hand side

Akhmetov M. U.

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Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1587–1594

A method for the investigation of differential equations with a nonclassical right-hand side [1] is applied to the study of the higher-order differentiability of solutions of differential equations with discontinuous right-hand sides with respect to the initial data. We use results from the theory of differential equations with pulse influence [2].

Article (Russian)

On a comparison method for pulse systems in the space $R^n$

Akhmetov M. U., Perestyuk N. A.

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Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 753–762

A method for the study of differential equations with pulse influence on the surfaces, which was realized in [1] for a bounded domain in the phase space, is now extended to the entire space $R^n$. We prove theorems on the existence of integral surfaces in the critical case and justify the reduction principle for these equations.

Brief Communications (Russian)

On the expansion of solutions to differential equations with discontinuous right-hand side in a series in initial data and parameters

Akhmetov M. U.

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Ukr. Mat. Zh. - 1993. - 45, № 5. - pp. 715–717

The conditions under which the solutions of equations with discontinuous right-hand sides depend on the initial data and parameters analytically are investigated. A definition is introduced, which specifies this dependence in the case where a surface of discontinuity exists.

Article (Russian)

Periodic solutions of strongly nonlinear systems with nonclassical right-hand side in the case of a family of generating solutions

Akhmetov M. U.

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Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 202–208

The problem of the existence of periodic solutions to differential equations with pulse effects on the surfaces and to differential equations with discontinuous right-hand sides close to arbitrary nonlinear ones is studied. The existence of a family of periodic solutions to generating equations is assumed.

Article (Ukrainian)

Asymptotic representation of solutions of regularly perturbed systems of differential equations with nonclassical right-hand side

Akhmetov M. U., Perestyuk N. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 1298–1304

Article (Ukrainian)

Stability of periodic solutions of differential equations with impulse action on surfaces

Akhmetov M. U., Perestyuk N. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 12. - pp. 1596–1601

Article (Ukrainian)

Differentiable dependence of the solutions of impulse systems on initial data

Akhmetov M. U., Perestyuk N. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 8. - pp. 1028–1033

Article (Ukrainian)

Almost-periodic solutions of impulse systems

Akhmetov M. U., Perestyuk N. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 1. - pp. 74-80

Article (Ukrainian)

Almost-periodic solutions of one class of systems with impulses

Akhmetov M. U., Perestyuk N. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 486 – 490