2018
Том 70
№ 8

All Issues

Trofimchuk S. I.

Articles: 20
Anniversaries (Ukrainian)

Anatolii Mykhailovych Samoilenko (on his 80th birthday)

Antoniouk A. Vict., Berezansky Yu. M., Boichuk A. A., Gutlyanskii V. Ya., Khruslov E. Ya., Kochubei A. N., Korolyuk V. S., Kushnir R. M., Lukovsky I. O., Makarov V. L., Marchenko V. O., Nikitin A. G., Parasyuk I. O., Pastur L. A., Perestyuk N. A., Portenko N. I., Ronto M. I., Sharkovsky O. M., Tkachenko V. I., Trofimchuk S. I.

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Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 3-6

Anniversaries (Ukrainian)

Oleksandr Mykolaiovych Sharkovs’kyi (on his 80th birthday)

Fedorenko V. V., Ivanov А. F., Khusainov D. Ya., Kolyada S. F., Maistrenko Yu. L., Parasyuk I. O., Pelyukh G. P., Romanenko O. Yu., Samoilenko V. G., Shevchuk I. A., Sivak A. G., Tkachenko V. I., Trofimchuk S. I.

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Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 257-260

Article (Ukrainian)

On sharp conditions for the global stability of a difference equation satisfying the Yorke condition

Nenya O. I., Tkachenko V. I., Trofimchuk S. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 73–80

Continuing our previous investigations, we give simple sufficient conditions for global stability of the zero solution of the difference equation xn+1 = qxn + fn (xn ,..., xn-k ), n ∈ Z, where nonlinear functions fn satisfy the Yorke condition. For every positive integer k, we represent the interval (0, 1] as the union of [(2k + 2) /3] disjoint subintervals, and, for q from each subinterval, we present a global-stability condition in explicit form. The conditions obtained are sharp for the class of equations satisfying the Yorke condition.

Article (Russian)

The theory of the numerical-analytic method: Achievements and new trends of development. VII

Ronto M. I., Samoilenko A. M., Trofimchuk S. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 9. - pp. 1244–1261

For the numerical-analytic method suggested by A. M. Samoilenko in 1965, we analyze the application to abstract differential equations, implicit equations, and control problems.

Article (Russian)

The theory of the numerical-analytic method: Achievements and new trends of development. VI

Ronto M. I., Samoilenko A. M., Trofimchuk S. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 960–971

We analyze the application of the numerical-analytic method proposed by A.M. Samoilenko in 1965 to multipoint boundary-value problems.

Article (Russian)

The theory of the numerical-analytic method: Achievements and new trends of development. V

Ronto M. I., Samoilenko A. M., Trofimchuk S. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 5. - pp. 663–673

We analyze the application of the numerical-analytic method proposed by A. M. Samoilenko in 1965 to difference equations.

Article (Russian)

The theory of the numerical-analytic method: Achievements and new trends of development. IV

Ronto M. I., Samoilenko A. M., Trofimchuk S. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1656–1672

We analyze the application of the numerical-analytic method proposed by Samoilenko in 1965 to autonomous systems of differential equations and impulsive equations.

Article (Russian)

The theory of the numerical-analytic method: Achievements and new trends of development. III

Ronto M. I., Samoilenko A. M., Trofimchuk S. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 960–979

We analyze results concerning the application of the numerical-analytic method suggested by Samoilenko to delay differential equations, differential equations with “maxima,” functional-differential, operator-differential, and integro-differential equations.

Article (Russian)

The theory of the numerical-analytic method: Achievements and new trends of development. II

Ronto M. I., Samoilenko A. M., Trofimchuk S. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 2. - pp. 225–243

We analyze results concerning the application of the numerical-analytic method suggested by Samoilenko in 1965 to second-order differential equations.

Anniversaries (Ukrainian)

Anatolii Mikhailovich Samoilenko (on his 60th birthday)

Berezansky Yu. M., Boichuk A. A., Korneichuk N. P., Korolyuk V. S., Koshlyakov V. N., Kulik V. L., Luchka A. Y., Mitropolskiy Yu. A., Pelyukh G. P., Perestyuk N. A., Skorokhod A. V., Skrypnik I. V., Tkachenko V. I., Trofimchuk S. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 3–4

Article (Russian)

The theory of the numerical-analytic method: Achievements and new trends of development. I

Ronto M. I., Samoilenko A. M., Trofimchuk S. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 102–117

We describe the history of the development of the numerical-analytic method suggested by Samoilenko in 1965 and analyze the relation of this method to other investigations.

Article (Ukrainian)

Spaces of piecewise-continuous almost-periodic functions and of almost-periodic sets on the line. I

Samoilenko A. M., Trofimchuk S. I.

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Ukr. Mat. Zh. - 1991. - 43, № 12. - pp. 1613–1619

Article (Ukrainian)

Unbounded functions with almost periodic differences

Samoilenko A. M., Trofimchuk S. I.

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Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 1409–1413

Article (Ukrainian)

Generalized solutions of impulse systems and the phenomenon of pulsations

Perestyuk N. A., Samoilenko A. M., Trofimchuk S. I.

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Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 657–663

Article (Ukrainian)

Impulse systems with fixed moments of shocks of general position: The structure of the set of moments of the shocks

Trofimchuk E. P., Trofimchuk S. I.

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Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 378–383

Article (Ukrainian)

Impulse systems with fixed shock times of general disposition: Existence, uniqueness of solution, and the well-posedness of the Cauchy problem

Trofimchuk E. P., Trofimchuk S. I.

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Ukr. Mat. Zh. - 1990. - 42, № 2. - pp. 230–237

Article (Ukrainian)

Bounded and periodic solutions of weakly nonlinear impulse evolutionary systems.

Rogovchenko Yu. V., Trofimchuk S. I.

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Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 260–264

Article (Ukrainian)

A criterion for ?rough? diagonalizability of systems of linear extensions of compact fluxes

Trofimchuk S. I.

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Ukr. Mat. Zh. - 1985. - 37, № 4. - pp. 523–527

Article (Ukrainian)

Linear extensions that satisfy the transversality condition

Trofimchuk S. I.

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Ukr. Mat. Zh. - 1984. - 36, № 6. - pp. 802 – 804

Article (Ukrainian)

A necessary condition for existence of an invariant manifold of a linear extension of a dynamic system on a compact manifold

Trofimchuk S. I.

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Ukr. Mat. Zh. - 1984. - 36, № 3. - pp. 390 - 393