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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 7, Pages 1201–1223
DOI: https://doi.org/10.31857/S0044466920050130 (Mi zvmmf11105) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Spectral estimates for the fourth-order operator with matrix coefficients

D. M. Polyakov

Southern Mathematical Institute, Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, 362027 Russia
Citations (7)
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DOI: https://doi.org/10.31857/S0044466920050130
Abstract: The fourth-order differential operator with matrix coefficients with the domain determined by quasi-periodic boundary conditions is considered. For this operator, the asymptotics of the arithmetic mean of the eigenvalues is found. Moreover, for various special cases, the asymptotics of the eigenvalues is also obtained. The spectral characteristics in the case of periodic and antiperiodic boundary conditions are studied separately. The results are better than those known before.
Key words: fourth-order differential operator, asymptotics of eigenvalues, matrix coefficients, arithmetic mean of eigenvalues.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation МК-1056.2018.1
This work was supported by President of the Russian Federation for young candidates of science, project nos. MK-1056.2018.1, 075-02-2018-433, and 075-15-2019-848.
Received: 24.01.2019
Revised: 02.12.2019
Accepted: 10.03.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 7, Pages 1163–1184
DOI: https://doi.org/10.1134/S0965542520050139
Bibliographic databases:
Document Type: Article
UDC: 517.927
Language: Russian
Citation: D. M. Polyakov, “Spectral estimates for the fourth-order operator with matrix coefficients”, Zh. Vychisl. Mat. Mat. Fiz., 60:7 (2020), 1201–1223; Comput. Math. Math. Phys., 60:7 (2020), 1163–1184
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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