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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, Volume 31, Issue 1, Pages 59–69
DOI: https://doi.org/10.35634/vm210105
(Mi vuu755)
 

This article is cited in 6 scientific papers (total in 6 papers)

MATHEMATICS

The absence of residual property for strong exponents of oscillation of linear systems

A. Kh. Stash

Adyghe State University, ul. Pervomaiskaya, 208, Maikop, 385000, Russia
Full-text PDF (171 kB) Citations (6)
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Abstract: In this paper, we study various types of exponents of oscillation (upper or lower, strong or weak) of zeros, roots, hyperroots, strict and non-strict signs of non-zero solutions of linear homogeneous differential systems on the positive semi-axis. On the set of non-zero solutions of autonomous systems the relations between these exponents of oscillation are established. It is proved that all strong exponents of oscillations (unlike Sergeev's frequencies of sign changes, zeros and roots, as well as all the weak exponents of oscillations) considered as functions on the set of solutions to linear homogeneous $n$-dimensional differential systems with continuous coefficients on the semi-line are not residual (i.e. can be changed when changing solution on a finite interval). Besides, at any beforehand given natural $n\geqslant2$ we give the example of $n$-dimensional differential system, for some solution of which all strong oscillation exponents differ from corresponding weak exponents. In this case, all weak and all strong exponents on the chosen solution coincide with each other, respectively. When proving the results of this work, the case of parity and odd $n$ are considered separately.
Keywords: differential equations, linear systems, oscillation, number of zeros, exponents of oscillation, Sergeev's frequencies.
Received: 11.12.2020
Bibliographic databases:
Document Type: Article
UDC: 517.926
MSC: 34C10
Language: Russian
Citation: A. Kh. Stash, “The absence of residual property for strong exponents of oscillation of linear systems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:1 (2021), 59–69
Citation in format AMSBIB
\Bibitem{Sta21}
\by A.~Kh.~Stash
\paper The absence of residual property for strong exponents of oscillation of linear systems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2021
\vol 31
\issue 1
\pages 59--69
\mathnet{http://mi.mathnet.ru/vuu755}
\crossref{https://doi.org/10.35634/vm210105}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    Abstract page:205
    Full-text PDF :133
    References:23
     
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