2018
Том 70
№ 6

All Issues

Ronto A. M.

Articles: 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.

Article (Ukrainian)

General conditions for the unique solvability of initial-value problem for nonlinear functional differential equations

Dil'na N. Z., Ronto A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 2. - pp. 167–172

We establish general conditions for the unique solvability of the Cauchy problem for systems of nonlinear functional differential equations.

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)

Some new conditions for the solvability of the cauchy problem for systems of linear functional-differential equations

Dil'na N. Z., Ronto A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 7. - pp. 867–884

We establish efficient conditions sufficient for the unique solvability of certain classes of Cauchy problems for systems of linear functional-differential equations. The conditions obtained are optimal in a certain sense.

Article (Russian)

Exact Solvability Conditions for the Cauchy Problem for Systems of First-Order Linear Functional-Differential Equations Determined by $(σ_1, σ_2, ... , σ_n; τ)$-Positive Operators

Ronto A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 11. - pp. 1541-1568

We obtain new sufficient conditions under which the Cauchy problem for a system of linear functional-differential equations is uniquely solvable for arbitrary forcing terms. The conditions established are unimprovable in a certain sense.

Article (Russian)

On the Periods of Periodic Motions in Autonomous Systems

Ronto A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 94-112

We obtain certain estimates for the periods of periodic motions in Lipschitz dynamical systems.