Roza Uteshova

• PhD
• Leading Researcher at Institute of Mathematics and Mathematical Modeling

The averaging method is applied to the study of optimal control problems for systems of integro-differential equations with rapidly oscillating coefficients and a small parameter. The original problem is associated with an averaged optimal control problem, formulated for a system of ordinary differential equations, which significantly simplifies th...

This paper addresses the solvability of two-point boundary value problems for linear differential-algebraic equations with time-varying coefficients. The proposed method employs the standard canonical form to decouple the system into an ordinary differential part and an algebraic part. By introducing an appropriate parameter, we transform the origi...

This paper addresses the approximation of a bounded (on the entire real axis) solution of a linear ordinary differential equation, where the matrix approaches zero as t →∓∞ and the right-hand side is bounded with a weight. We construct regular two-point boundary value problems to approximate the original problem, assuming the matrix and the right-h...

UDC 517.9 We consider a two-point boundary-value problem for a system of differential equations with generalized piecewise-constant argument. To solve the problem, we propose to use a constructive method based on the Dzhumabaev parametrization method and a new approach to the concept of general solution. The interval is partitioned with regard for...

We study a two-point boundary value problem for a linear differential-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of the solution at the left endpoint of the interval. Applying the Weierstrass canonical form to the matrix pair a...

This study deals with a boundary value problem for a linear Fredholm integro-differential equation subject to impulse effects at fixed time points. The interval is partitioned which that the set of partition points contains the points of impulse and the values of the desired function at the left-end points of the subintervals are introduced as para...

We study a two-point boundary value problem for a linear differen\-tial-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of the solution at the left endpoint of the interval. Applying the Weierstrass canonical form to the matrix pair...

This paper deals with a Fredholm integro-differential equation with non-linear integral term. By using the Dzhumabaev parametrization method, we reduce the equation to a special Cauchy problem and establish sufficient conditions for the existence of its unique solution. The solution to the special Cauchy problem is used to construct a new general sol...

The article considers a nonlinear boundary value problem for a linear delay differential equation. To solve the problem, the idea of parametrization method, namely, the interval at which the problem is being considered, is divided into subintervals whose lengths do not exceed the values of the constant delay; constant parameters are introduced at t...

This study deals with a boundary-value problem for a linear Fred-holm integro-differential equation subject to impulse effects at fixed time points. Solvability criteria are provided in terms of input data, without the use of a fundamental matrix and a resolvent. We also propose an algorithm to solve the problem under consideration, establish its c...

This paper studies oscillatory properties of solutions of a dynamic equation on the set of time scales Tλ provided that the graininess function µλ approaches zero as λ → 0. We derived the conditions under which oscillation of solutions of differential equations implies that of solutions of the corresponding equations defined on time scales with the...

This paper deals with a problem of finding a bounded solution of a system of nonhomogeneous linear differential equations with an unbounded matrix of coefficients on a finite interval. The right-hand side of the equation belongs to a space of continuous functions bounded with some weight; the weight function is chosen taking into account the behavi...

This paper proposes an effective method for solving a nonlocal problem for a system of second-order hyperbolic equations with piecewise constant time argument of generalized type. The method is based on the introduction of functional parameters that are set as the values of the desired solution along the lines of the domain partition with respect t...

In this work, we propose a new computational approach is implemented to solve a two-point BVP for a loaded differential equation with piecewise constant argument of generalized type (DEPCAG) based on the Dzhumabaev parameterization method. In this method, as parameters, we take the values of the desired solution at the partition points which are ch...

The method of averaging is applied to study the existence of solutions of boundary value problems for systems of differential equations with non-fixed moments of impulse action. It is shown that if an averaged boundary value problem has a solution, then the original problem is solvable as well. Here the averaged problem for the impulsive system is...

In this paper, we propose an algorithm for solving a two-point boundary-value problem for a linear differential equation with constant delay subject to a nonlinear boundary condition. We derive sufficient conditions for the convergence of the algorithm and for the existence of an isolated solution to the problem under study. A numerical example is...

The paper deals with a nonlinear ordinary differential equation with singularities at the end-points of a finite interval. The definition of a limit with a weight solution is introduced and its attracting property is established. A singular boundary value problem for the differential equation is studied, where the boundary condition imposed on a so...

A linear boundary value problem for a system of integro-differential equations with involution is studied by the parameterization method. Sufficient conditions for the existence of a unique solution to the problem are established in terms of coefficients. An algorithm for finding the solution to the problem under consideration is proposed.

This paper deals with a problem of finding a bounded in a strip solution to a system of second order hyperbolic evolution equations, where the matrix coefficient of the spatial derivative tends to zero as t→∓∞. The problem is studied under assumption that the coefficients, the right-hand side of the system, and the boundary function belong to some...

This article presents a computational method for solving a problem with parameter for a system of Fredholm integro-differential equations. Some additional parameters are introduced and the problem under consideration is reduced to solving a system of linear algebraic equations. The coefficients and right-hand side of the system are calculated by so...

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