Kostin A. V.
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
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