Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2018, Number 6, Pages 46–58 (Mi vmumm584)  
This article is cited in 7 scientific papers (total in 7 papers)

Mathematics

Asymptotics of eigenvalues of fourth order differential operator with alternating weight function

S. I. Mitrokhin

Lomonosov Moscow State University, Research Computing Center
Full-text PDF (385 kB) Citations (7)
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Abstract: We study a fourth-order differential operator with a sign-alternating weight function with separated boundary conditions. For large values of the spectral parameter the asymptotics of the solutions to the corresponding differential equations is derived. The study of boundary conditions makes it possible to obtain an equation for eigenvalues of the considered differential operator. The indicator diagram of this equation is studied. The asymptotics of eigenvalues in various sectors of the indicator diagram is obtained.
Key words: differential operator, spectral parameter, boundary conditions, sign-alternating weight function, indicator diagram, asymptotics of eigenvalues.
Received: 14.02.2018
English version:
Moscow University Mathematics Bulletin, 2018, Volume 73, Issue 6, Pages 254–265
DOI: https://doi.org/10.3103/S0027132218060074
Bibliographic databases:
Document Type: Article
UDC: 517.927
Language: Russian
Citation: S. I. Mitrokhin, “Asymptotics of eigenvalues of fourth order differential operator with alternating weight function”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, no. 6, 46–58; Moscow University Mathematics Bulletin, 73:6 (2018), 254–265
Citation in format AMSBIB
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