# Kostin A. V.

### Problem of shadow in the Lobachevski space

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 11. - pp. 1525-1532

We consider the problem of shadow in a hyperbolic space. This problem can be regarded as a problem of finding conditions guaranteeing that points belong to a generalized convex hull of the family of balls.

### On solutions of a second-order quasilinear differential system representable by Fourier series with slowly varying parameters

Kostin A. V., Shchegolev S. A.

Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 654–664

For a second-order quasilinear differential system whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove that, under certain conditions, there exists a particular solution with a similar structure in the case of purely imaginary roots of the characteristic equation for the matrix of coefficients of the linear part.

### On asymptotic decompositions of *o*-solutions in the theory of quasilinear systems of difference equations

Ukr. Mat. Zh. - 1997. - 49, № 5. - pp. 672–677

We consider a quasilinear system of difference equations with certain conditions. We prove that there exists a formal partial *o*-solution of this system in the form of functional series of special type. We also prove a theorem on the asymptotic behavior of this solution.

### On single-value solutions of nonlinear differential equations of the first order and some properties of real periodic solutions

Ukr. Mat. Zh. - 1964. - 16, № 1. - pp. 110-115