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Mat. Sb., 2014, Volume 205, Number 5, Pages 77–96 (Mi msb8298)  

This article is cited in 1 scientific paper (total in 1 paper)

The continuous spectrum and the effect of parametric resonance. The case of bounded operators

V. V. Skazkaab

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

Abstract: The paper is concerned with the Mathieu-type differential equation $u–A^2 u+\varepsilon B(t)u$ in a Hilbert space $H$. It is assumed that $A$ is a bounded self-adjoint operator which only has an absolutely continuous spectrum and $B(t)$ is almost periodic operator-valued function. Sufficient conditions are obtained under which the Cauchy problem for this equation is stable for small $\varepsilon$ and hence free of parametric resonance.
Bibliography: 10 titles.

Keywords: parametric resonance, continuous spectrum, stability.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Siberian Branch of Russian Academy of Sciences


DOI: https://doi.org/10.4213/sm8298

Full text: PDF file (540 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:5, 684–702

Bibliographic databases:

UDC: 517.928
MSC: 34D05, 47A10, 70K28
Received: 08.11.2013

Citation: V. V. Skazka, “The continuous spectrum and the effect of parametric resonance. The case of bounded operators”, Mat. Sb., 205:5 (2014), 77–96; Sb. Math., 205:5 (2014), 684–702

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8298
  • http://mi.mathnet.ru/eng/msb/v205/i5/p77

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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, “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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