Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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The Asymptotics of the Eigenvalues of the Model Boundary Value Problem for Differential Operator of High Order with Summable Potential

Author(s):

Sergey Ivanovich Mitrokhin

Research Computer Center of
Lomonosov Moscow State University,
senior researcher,
Moscow, Vorobyovy Gory, 1
associate Professor, Professor of RAE,
PhD in physics and mathematics

mitrokhin-sergey@yandex.ru

Abstract:

The boundary value problem for a family of differential operators with separated boundary conditions is studied. The potential of a differential operator is a summable function on the segment. The asymptotic of solutions of the corresponding differential equations for large values of the spectral parameter is obtained. The equation for the eigenvalues of the studied operators is deduced. The asymptotic behavior of the eigenvalues of the studied family of differential operators is found. The equation to which the eigenfunctions of the studied operators satisfy is obtained.

Keywords

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