Asymptotic methods of nonlinear mechanics developed by N. M. Krylov and
N. N. Bogoliubov originated new trend in perturbation theory. They pene-
trated deep into various applied branches (theoretical physics,
mechanics, ap- plied astronomy, dynamics of space flights, and others)
and laid the founda- tion for lrumerous generalizations and for the
creation of various modifications of thesem. E!f, hods. A great number
of approaches and techniques exist and many differen. t classes of
mathematical objects have been considered (ordinary differential
equations, partial differential equations, delay diffe, 'ential
equations and others). The stat. e of studying related problems was
described in mono- graphs and original papers of Krylov N. M.,
Bogoliubov N. N. [1], [2], Bogoli- ubov N. N [1J, Bogoliubov N. N.,
Mitropolsky Yu. A. [1], Bogoliubov N. N., Mitropol- sky Yu. A.,
Samoilenko A. M. [1], Akulenko L. D. [1], van den Broek B. [1],
van den Broek B., Verhulst F. [1], Chernousko F. L., Akulenko L. D.
and Sokolov B. N. [1], Eckhause W. [l], Filatov A. N. [2], Filatov
A. N., Shershkov V. V. [1], Gi- acaglia G. E. O. [1], Grassman J.
[1], Grebennikov E. A. [1], Grebennikov E. A., Mitropolsky Yu. A.
[1], Grebennikov E. A., Ryabov Yu. A. [1], Hale J . K. [I]' Ha-
paev N. N. [1], Landa P. S. [1), Lomov S. A. [1], Lopatin A. K.
[22]-[24], Lykova O. B.