RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2013, Volume 94, Issue 1, Pages 55–67 (Mi mz10230)  

This article is cited in 5 scientific papers (total in 5 papers)

Spectral and Oscillatory Properties of a Linear Pencil of Fourth-Order Differential Operators

J. Ben Amaraa, A. A. Vladimirovb, A. A. Shkalikovc

a University of 7-th November at Carthage
b Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
c M. V. Lomonosov Moscow State University

Abstract: The paper deals with the spectral and oscillatory properties of a linear operator pencil $A-\lambda B$, where the coefficient $A$ corresponds to the differential expression $(py")"$ and the coefficient $B$ corresponds to the differential expression $-y"+cry$. In particular, it is shown that all negative eigenvalues of the pencil are simple and, under some additional conditions, the number of zeros of the corresponding eigenfunctions is related to the serial number of the corresponding eigenvalue.

Keywords: linear differential operator, initial boundary-value problem, pencil of operators, number of zeros of eigenfunctions.

DOI: https://doi.org/10.4213/mzm10230

Full text: PDF file (555 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2013, 94:1, 49–59

Bibliographic databases:

UDC: 517.984
Received: 09.02.2011
Revised: 28.12.2012

Citation: J. Ben Amara, A. A. Vladimirov, A. A. Shkalikov, “Spectral and Oscillatory Properties of a Linear Pencil of Fourth-Order Differential Operators”, Mat. Zametki, 94:1 (2013), 55–67; Math. Notes, 94:1 (2013), 49–59

Citation in format AMSBIB
\Bibitem{BenVlaShk13}
\by J.~Ben Amara, A.~A.~Vladimirov, A.~A.~Shkalikov
\paper Spectral and Oscillatory Properties of a Linear Pencil of Fourth-Order Differential Operators
\jour Mat. Zametki
\yr 2013
\vol 94
\issue 1
\pages 55--67
\mathnet{http://mi.mathnet.ru/mz10230}
\crossref{https://doi.org/10.4213/mzm10230}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3206067}
\zmath{https://zbmath.org/?q=an:06228528}
\elib{http://elibrary.ru/item.asp?id=20731757}
\transl
\jour Math. Notes
\yr 2013
\vol 94
\issue 1
\pages 49--59
\crossref{https://doi.org/10.1134/S0001434613070055}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000323665000005}
\elib{http://elibrary.ru/item.asp?id=20456351}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84883435240}


Linking options:
  • http://mi.mathnet.ru/eng/mz10230
  • https://doi.org/10.4213/mzm10230
  • http://mi.mathnet.ru/eng/mz/v94/i1/p55

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. Ch. Kulaev, “On the Oscillation Property of Green's Function of a Fourth-Order Discontinuous Boundary-Value Problem”, Math. Notes, 100:3 (2016), 391–402  mathnet  crossref  crossref  mathscinet  isi  elib
    2. D. B. Nurakhmetov, S. A. Jumabayev, A. A. Aniyarov, “Inverse boundary problems for intermediate springs on a rod with geometrical symmetry”, Electron. J. Differential Equations, 2017, 33, 10 pp.  mathscinet  zmath  isi
    3. L. A. Vlasenko, A. G. Rutkas, “Optimal Control of Undamped Sobolev-Type Retarded Systems”, Math. Notes, 102:3 (2017), 297–309  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Sergey M. Zagorodnyuk, “The Inverse Spectral Problem for Jacobi-Type Pencils”, SIGMA, 13 (2017), 085, 16 pp.  mathnet  crossref
    5. S. M. Zagorodnyuk, “Difference equations related to Jacobi-type pencils”, J. Differ. Equ. Appl., 24:10 (2018), 1664–1684  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:877
    Full text:109
    References:85
    First page:87

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019