This article is cited in 14 papers

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

J. Ben Amara^a, A. A. Vladimirov^b, A. A. Shkalikov<sup>c

a</sup> 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.

UDC: 517.984

Received: 09.02.2011
Revised: 28.12.2012

DOI: 10.4213/mzm10230

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

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