  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
$(0,1)$.
