Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zhurnal SVMO:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2020, Volume 22, Number 3, Pages 280–305
DOI: https://doi.org/10.15507/2079-6900.22.202003.280-305
(Mi svmo773)
 

Mathematics

On the asymptotic behavior of the spectrum of a sixth-order differential operator, whose potential is the delta function

S. I. Mitrokhin

Lomonosov Moscow State University, Research Computing Center
References:
Abstract: In this paper we propose a new method for studying differential operators with discontinuous coefficients. We consider a sequence of sixth-order differential operators with piecewise-smooth coefficients. The limit of the sequence of these operators’ potentials is the Dirac delta function. The boundary conditions are separated. To correctly determine solutions of differential equations with discontinuous coefficients at the points of discontinuity, “gluing” conditions are required. Asymptotic solutions were written out for large values of the spectral parameter, with the help of them the “gluing” conditions were studied and the boundary conditions were investigated. As a result, we derive an eigenvalues equation for the operator under study, which is an entire function. The indicator diagram of the eigenvalues equation, which is a regular hexagon, is investigated. In various sectors of the indicator diagram, the method of successive approximations has been used to find the eigenvalues asymptotics of the studied differential operators. The limit of the asymptotic of the spectrum determines the spectrum of the sixth-order operator, whose potential is the delta function.
Keywords: differential operator with discontinuous coefficients, asymptotic behavior of solutions, piecewise-smooth potential, Dirac delta function, asymptotic behavior of eigenvalues, spectrum of an operator.
Document Type: Article
UDC: 517.9
MSC: Primary 34L20; Secondary 34B40, 47E05
Language: Russian
Citation: S. I. Mitrokhin, “On the asymptotic behavior of the spectrum of a sixth-order differential operator, whose potential is the delta function”, Zhurnal SVMO, 22:3 (2020), 280–305
Citation in format AMSBIB
\Bibitem{Mit20}
\by S.~I.~Mitrokhin
\paper On the asymptotic behavior of the spectrum of a~sixth-order differential operator, whose potential is~the~delta function
\jour Zhurnal SVMO
\yr 2020
\vol 22
\issue 3
\pages 280--305
\mathnet{http://mi.mathnet.ru/svmo773}
\crossref{https://doi.org/10.15507/2079-6900.22.202003.280-305}
Linking options:
  • https://www.mathnet.ru/eng/svmo773
  • https://www.mathnet.ru/eng/svmo/v22/i3/p280
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024