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

J. Ben Amara; A. A. Shkalikov; A. A. Vladimirov

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arXiv · 1112.2351

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

J. Ben Amara·A. A. Shkalikov·A. A. Vladimirov

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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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BibTeX RIS

J. Ben Amara, A. A. Shkalikov, A. A. Vladimirov. 2011-12-11. Spectral and oscillation properties for a linear pencil of fourth-order differential operators. https://arxiv.org/abs/1112.2351

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