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.
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