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

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

2011-12-11

arxiv.org/abs/1112.2351v1

Mathematics

Spectral Theory

12 pages

Scientific paper

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 $(0,1)$.

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