Spectral and oscillation properties for a linear pencil of fourth-order differential operators

2011/12/11 by Amara, J. Ben, Shkalikov, A. A., Vladimirov, A. A.
#34B09 #34L20 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1112.2351

Abstract

The present paper deals with the spectral and the oscillation properties of a linear pencil A-λB. Here A and B are linear operators generated by the differential expressions (py")" and -y"+ cry, respectively. In particular, it is shown that the negative eigenvalues of this problem are simple and the corresponding eigenfunctions y_-n have n-1 zeros in (0,1).

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