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Approximation of nonstationary processes on an infinite time interval for exponential stability of slow motions. (English. Russian original) Zbl 0442.34054

J. Appl. Math. Mech. 43, 237-246 (1980); translation from Prikl. Mat. Mekh. 43, 219-228 (1979).

MSC:

34E05 Asymptotic expansions of solutions to ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
Full Text: DOI

References:

[1] Zabreiko, P. P.; Ledovskaia, I. B., On the proof of the Bogoliubov-Krylov method for ordinary differential equations, Differents. Uravn., Vol. 5, No. 2 (1969)
[2] Mirkina, A. S., On a modification of the averaging method and estimates of higher approximations, PMM, Vol. 41, No. 5 (1977) · Zbl 0404.34036
[3] A1ekseev, V. M., On an estimate of the perturbations of solutions of ordinary differential equations, I. Vestn. Moskovsk. Gos. Univ., Ser. Mat., Mekh, No. 2 (1961)
[4] Krasnosel’skii, M. A., Operator of Displacement Over the Trajectories of Differential Equations (1966), Nauka: Nauka Moscow · Zbl 0149.05201
[5] Mitropol’skii, Iu. A.; Lykova, O. B., Integral Manifolds and Nonlinear Mechanics (1973), Nauka: Nauka Moscow
[6] Feshchenko, S. F.; Shkil’, N. I.; Nikolenko, L. D., Asymptotic Methods in the Theory of Linear Differential Equations (1966), Naukova Dumka: Naukova Dumka Kiev · Zbl 0141.28004
[7] Volosov, V. M., Averaging in systems of ordinary differential equations, Uspekhi Mat. Nauk, Vol. 17, No. 6 (1962) · Zbl 0119.07502
[8] Reimers, N. A.; Khodzhaev, K. Sh., Averaging of quasilinear systems with many fast variables, Differents. Uravn., Vol. 14, No. 8 (1978) · Zbl 0475.34026
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