Asymptotic method for the investigation of m-frequency oscillation systems

We describe an asymptotic method for the integration of m-frequency oscillation systems of order 2n, analyze averaged equations in nonresonance and resonance cases, prove a theorem on the preservation of smooth p-dimensionai invariant tori under perturbation for any 0 ≤ p ≤ n, and indicate forms of decomposable m-frequency oscillation systems. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1366–1387, October, 1998.     

On Extendability of Solutions of Differential Equations to a Singular Set

We consider the problem of the extendability of solutions of differential equations to a singular set that consists of points at which the right-hand side of the equation considered is undefined.     

Mykola Ivanovych Portenko (On His 60th Birthday)

Ukrainian Mathematical Journal -     

Mykola Ivanovych Shkil' (On His 70th Birthday)

Ukrainian Mathematical Journal -     

Improvement of the technology for reprocessing black liquors from kraft pulp production

A way to improve the kraft pulp production process via acid–base treatment of black liquor was suggested. Data on the process for kraft lignin production by the sulfuric acid procedure were substantiated.     

Quasiperiodic Solutions of Differential-Difference Equations on a Torus

This paper is dedicated to Professor V. A. Pliss on his 70th birthday. In connection with problems considered here, one should note the famous result of V. A. Pliss concerning the structural stability of differential equations on a torus. The first part of the present paper is devoted to the extension to differential-difference equations on an m-dimensional torus of the V. I. Arnold's result [1] about the reducibility of analytic systems on an m-dimensional torus to pure rotation. This result of Arnold was first extended to smooth systems of differential equations on an m-dimensional torus by A. M. Samoilenko [2] and later, independently, by J. Moser [3]. The Nash smoothing method, which was used in [2] (as indicated in [3-5]), leads to a large loss of smoothness. In the second part of the present paper, we use the Moser method of approximation of smooth functions by analytic ones for the reduction of smooth differential-difference equations on an m-dimensional torus to the canonical form $$\dot \phi (t) = \omega + f(\phi (t),\;\phi (t - h)),{\text{}}f(\phi ,\;\phi - \omega h) = 0.$$ Note that the considered problem of investigation of differential-difference equations on an m-dimensional torus is important in theory [6, 7]. Moreover, the results obtained can be used for in the investigation of multifrequency oscillations of retarded systems.     

Boundary-value problems for differential equations unresolved with respect to the derivative in the space of bounded number sequences

We study a nonlinear countable-point boundary-value problem for a differential equation unresolved with respect to the derivative. This equation and a nonlinear boundary condition are defined in the Banach space of bounded number sequences. We study the reducibility of the posed problem to a multipoint boundary-value problem in a finite-dimensional space. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 3, pp. 391–415, July–September, 2007.     

Solvability of a Cauchy Problem for Linear Integro-Differential Equations with Transformed Argument

We obtain sufficient conditions for the unique solvability of the initial-value problem for linear integro-differential equations. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 388–403, July–September, 2005