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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. , , Bogoli- ubov N. N [1J, Bogoliubov N. N. , Mitropolsky Yu. A. , Bogoliubov N. N. , Mitropol- sky Yu. A. , Samoilenko A. M. , Akulenko L. D. , van den Broek B. , van den Broek B. , Verhulst F. , Chernousko F. L. , Akulenko L. D. and Sokolov B. N. , Eckhause W. [l], Filatov A. N. , Filatov A. N. , Shershkov V. V. , Gi- acaglia G. E. O. , Grassman J. , Grebennikov E. A. , Grebennikov E. A. , Mitropolsky Yu. A. , Grebennikov E. A. , Ryabov Yu. A. , Hale J . K. [I]' Ha- paev N. N. , Landa P. S. [1), Lomov S. A. , Lopatin A. K. -, Lykova O. B.
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