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Mat. Sb., 2012, Volume 203, Number 3, Pages 3–22 (Mi msb7812)  

This article is cited in 5 scientific papers (total in 5 papers)

The spectral properties of distributions and asymptotic methods in perturbation theory

V. S. Belonosovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University

Abstract: 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, distributions, Fourier transform.

DOI: https://doi.org/10.4213/sm7812

Full text: PDF file (559 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:3, 307–325

Bibliographic databases:

UDC: 517.928
MSC: Primary 34C29; Secondary 46F05
Received: 01.11.2010

Citation: V. S. Belonosov, “The spectral properties of distributions and asymptotic methods in perturbation theory”, Mat. Sb., 203:3 (2012), 3–22; Sb. Math., 203:3 (2012), 307–325

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Skazka, “The continuous spectrum and the effect of parametric resonance. The case of bounded operators”, Sb. Math., 205:5 (2014), 684–702  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. N. A. Lyulko, N. A. Kudryavtseva, A. N. Kudryavtsev, “Asimptoticheskii i chislennyi analiz parametricheskogo rezonansa v nelineinoi sisteme dvukh ostsillyatorov”, Sib. elektron. matem. izv., 11 (2014), 675–694  mathnet
    3. N. A. Lyul'ko, “Instability of a nonlinear system of two oscillators under main and combination resonances”, Comput. Math. Math. Phys., 55:1 (2015), 53–70  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. V. S. Belonosov, “Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations”, Sb. Math., 208:8 (2017), 1088–1112  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. V. V. Skazka, “Stable perturbations of linear differential equations generating a uniformly bounded group”, Sb. Math., 208:8 (2017), 1246–1259  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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