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Matematicheskie Zametki, 2013, Volume 94, Issue 1, Pages 55–67
DOI: https://doi.org/10.4213/mzm10230 (Mi mzm10230) 		 
This article is cited in 12 scientific papers (total in 12 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
Full-text PDF (555 kB) Citations (12)
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DOI: https://doi.org/10.4213/mzm10230
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.
Received: 09.02.2011
Revised: 28.12.2012
English version:
Mathematical Notes, 2013, Volume 94, Issue 1, Pages 49–59
DOI: https://doi.org/10.1134/S0001434613070055
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
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
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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