Spectral and oscillation properties for a linear pencil of fourth-order   differential operators
  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 $(0,1)$. 
J. Ben Amara, A. A. Shkalikov, A. A. Vladimirov
math.SP