# Dzhumabaev D. S.

### New general solutions of ordinary differential equations and the methods of solving the boundary-value problems

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 7. - pp. 884-905

UDC 517.624

New general solutions of ordinary differential equations are introduced and their properties are established. We develop
new methods of solving the boundary-value problems based on the construction and solving of the systems of algebraic
equations for arbitrary vectors of the general solutions. An approach to finding the initial approximation to the solution of
a nonlinear boundary-value problem is proposed.

### Criteria for the existence of an isolated solution of a nonlinear boundary-value problem

Dzhumabaev D. S., Temesheva S. M.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 3. - pp. 356-365

A nonlinear two-point boundary-value problem for an ordinary differential equation is studied by the method of parametrization. We construct systems of nonlinear algebraic equations that enable us to find the initial approximation to the solution to the posed problem. In terms of the properties of constructed systems,we establish necessary and sufficient conditions for the existence of an isolated solution to the boundary-value problem under consideration.

### Weighted limit solution of a nonlinear differential equation at a singular point and its property

Dzhumabaev D. S., Uteshova R. E.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 12. - pp. 1717-1722

On a finite interval, we consider a system of nonlinear ordinary differential equations with a singularity at the left endpoint of the interval. The definition of weighted limit solution is introduced and its attracting property is established.

### Properties of the isolated solutions bounded on the entire axis for a system of nonlinear ordinary differential equations

Abildayeva A. D., Dzhumabaev D. S.

Ukr. Mat. Zh. - 2016. - 68, № 8. - pp. 1132-1138

We establish the conditions of continuous dependence on the right-hand side for the “isolated” solutions of a system of nonlinear ordinary differential equations bounded on the entire axis.

### Necessary and Sufficient Conditions for the Solvability of Linear Boundary-Value Problems for the Fredholm Integrodifferential Equations

Ukr. Mat. Zh. - 2014. - 66, № 8. - pp. 1074–1091

We propose a method for the investigation and solution of linear boundary-value problems for the Fredholm integrodifferential equations based on the partition of the interval and introduction of additional parameters. Every partition of the interval is associated with a homogeneous Fredholm integral equation of the second kind. The definition of regular partitions is presented. It is shown that the set of regular partitions is nonempty. A criterion for the solvability of the analyzed problem is established and an algorithm for finding its solutions is constructed.

### Periodic solutions of systems of hyperbolic equations bounded on a plane

Assanova A. T., Dzhumabaev D. S.

Ukr. Mat. Zh. - 2004. - 56, № 4. - pp. 562-572

For a linear system of hyperbolic equations of the second order with two independent variables, we investigate the problem of the existence and uniqueness of a solution periodic in both variables and a solution periodic in one of the variables and bounded on a plane. By using the method of introduction of functional parameters, we obtain sufficient conditions for the unique solvability of the problems under consideration.