Mitrokhin S.I. About the Spectral Properties of the Family of the Differential Operator of Even Order with Summable Potentia

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https://doi.org/10.15688/mpcm.jvolsu.2018.2.2

Sergey Ivanovich Mitrokhin
Candidate of Physical and Mathematical Sciences, Associate Professor,
Professor of Russian Academy of Natural Science,
Senior Researcher, Research Computing Center of Lomonosov
Moscow State University This email address is being protected from spambots. You need JavaScript enabled to view it.
Leninskie gory St., 1, bld. 4, 119992 Moscow, Russian Federation

Abstract. The article is devoted to investigating the method for studying the spectral properties of differential operators of high even order with summable potential. The asymptotic behavior of the solutions of the corresponding differential equation has been found for large values of the spectral parameter. The boundary conditions have been studied, and the equation for eigenvalues of the operator under investigation has been formulated. The indicator diagram of this equation has been studied. The asymptotic behavior of eigenvalues of the studied operator has been found.

Key words: differential operator, spectral parameter, boundary conditions, indicator diagram, asymptotics of eigenvalues.

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Mitrokhin S.I. About the Spectral Properties of the Family of the Differential Operator of Even Order with Summable Potentia by Mitrokhin S.I. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Citation in English: Mathematical Physics and Computer Simulation. Vol. 21 No. 2 2018, pp. 13-26

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