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

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

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

Spectral Theory 2011-12-13 v1

Authors: J. Ben Amara , A. A. Shkalikov , A. A. Vladimirov

Abstract

The present paper deals with the spectral and the oscillation properties of a linear pencil $A-\lambda B$ . 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 $(0,1)$ .

Keywords

linear pencil fourth-order differential operators spectral properties oscillation properties negative eigenvalues eigenfunctions

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@article{arxiv.1112.2351,
  title  = {Spectral and oscillation properties for a linear pencil of fourth-order differential operators},
  author = {J. Ben Amara and A. A. Shkalikov and A. A. Vladimirov},
  journal= {arXiv preprint arXiv:1112.2351},
  year   = {2011}
}

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12 pages

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

Abstract

Keywords

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