Geodesic
The spectral properties of distributions and asymptotic methods in perturbation theory
Sbornik. Mathematics, Tome 203 (2012) no. 3, pp. 307-325

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For differential equations of the form $x'=\varepsilon f(t,x;\varepsilon)$ in a Banach space a modification of the classical Krylov-Bogolyubov method is put forward. It allows complications in the construction of higher-order approximations which stem from the ‘small denominators problem’ to be avoided and many of the standard constraints on the behaviour of the function $f$ to be eliminated. The approach suggested is based on some results on the Fourier transforms of distributions. Bibliography: 17 titles.
Keywords: method of averaging, spectrum
Mots-clés : distributions, Fourier transform. 
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V. S. Belonosov. The spectral properties of distributions and asymptotic methods in perturbation theory. Sbornik. Mathematics, Tome 203 (2012) no. 3, pp. 307-325. http://geodesic.mathdoc.fr/item/SM_2012_203_3_a0/