2018
Том 70
№ 8

All Issues

Ronto M. I.

Articles: 17
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.

Full text (.pdf)

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

Article (English)

On solutions of nonlinear boundary-value problems the components of which vanish at certain points

Puza B., Ronto A. M., Ronto M. I., Shchobak N.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 94-114

We show how an appropriate parametrization technique and successive approximations can help to investigate nonlinear boundary-value problems for systems of differential equations under the condition that the components of solutions vanish at some unknown points. The technique can be applied to nonlinearities involving the signs of absolute value and positive or negative parts of functions under various types of boundary conditions.

Anniversaries (Ukrainian)

Fifty years devoted to science (on the 70th birthday of Anatolii Mykhailovych Samoilenko)

Berezansky Yu. M., Dorogovtsev A. A., Drozd Yu. A., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Mitropolskiy Yu. A., Perestyuk N. A., Rebenko A. L., Ronto A. M., Ronto M. I., Samoilenko Yu. S., Sharko V. V., Sharkovsky O. M.

Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 3–7

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.

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 (Russian)

Investigation and solution of boundary-value problems with parameters by numerical-analytic method

Korol' I. I., Ronto M. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1031–1042

We suggest a modification of the numerical-analytic iteration method. This method is used for studying the problem of existence of solutions and for constructing approximate solutions of nonlinear two-point boundary-value problems for ordinary differential equations with unknown parameters both in the equation and in boundary conditions.

Article (Ukrainian)

A numerical-analytic method for three-point boundary-value problems

Ronto M. I., Savina T. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 393–403

We suggest a modification of the numerical-analytic iteration method. This method is used for studying the problem of existence of solutions and for constructing approximate solutions of nonlinear ordinary differential systems with linear three-point boundary conditions of general form.

Article (Ukrainian)

Method of polynomial approximations for the investigation of boundary-value problems

Ronto M. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 518 – 522

Article (Ukrainian)

Convergence of the method of trigonometric collocation for nonlinear periodic systems of differential equations with retarded argument

Ronto M. I.

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Ukr. Mat. Zh. - 1983. - 35, № 6. - pp. 788–792

Article (Ukrainian)

Collocation method for a multipoint boundary-value problem

Ronto M. I.

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Ukr. Mat. Zh. - 1983. - 35, № 4. - pp. 524—527

Article (Ukrainian)

Application of the method of collocation to solve boundary value problems

Ronto M. I.

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Ukr. Mat. Zh. - 1971. - 23, № 3. - pp. 415–421

Brief Communications (Russian)

The periodic solution of a linear inhomogeneous differential equation

Ronto M. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1969. - 21, № 2. - pp. 265–267