Reducibility of a system of linear differential equations with quasiperiodic coefficients

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 12, pp.1669–1680, December, 1989.     

On the 70th birthday of Yurii Makarovich Berezanskii

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 579–582, May, 1995.     

Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution

We investigate the behavior of a diserete dynamical system in a neighborhood of a quasiperiodic trajeetory for the case of an infinite-dimensional Banach space We find conditions sufficient for the system considered to reduce, in such a neighborhood, to a system with quasiperiodic coefficients. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1661–1676, December, 1997.     

Asymptotic Solutions of a First-Order Differential Equation with Deviating Argument and Slowly Varying Coefficients

The object of this paper is to study the problem of constructing an approximate solution of a first-order weakly nonlinear ordinary differential equation with deviating argument and slowly varying coefficients. On the basis of asymptotic techniques in nonlinear mechanics, we construct an algorithm for the asymptotic integration of the differential equation under consideration.__________Published in Neliniini Kolyvannya, Vol. 7, No. 4, pp. 475–486, October–December, 2004.