Ronto A. M.
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.
General conditions for the unique solvability of initial-value problem for nonlinear functional differential equations
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.
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.
Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 3–7
Some new conditions for the solvability of the cauchy problem for systems of linear functional-differential equations
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.
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
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.
Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 94-112
We obtain certain estimates for the periods of periodic motions in Lipschitz dynamical systems.
On a method for construction of successive approximations for investigation of multipoint boundary-value problems
Ukr. Mat. Zh. - 1995. - 47, № 9. - pp. 1243–1253
We suggest a new scheme of successive approximations. This scheme allows one to study the problem of existence and approximate construction of solutions of nonlinear ordinary differential equations with multipoint linear boundary conditions. This method enables one to study problems both with singular and nonsingular matrices in boundary conditions.