  A family $\BA_\a$ of differential operators depending on a real parameter
$\a$ is considered. The problem can be formulated in the language of
perturbation theory of quadratic forms. The perturbation is only relatively
bounded but not relatively compact with respect to the unperturbed form.
  The spectral properties of the operator $\BA_\a$ strongly depend on $\a$. In
particular, for $\a<\sqrt2$ the spectrum of $\BA_\a$ below 1/2 is finite, while
for $\a>\sqrt2$ the operator has no eigenvalues at all. We study the asymptotic
behaviour of the number of eigenvalues as $\a\nearrow\sqrt2$. We reduce this
problem to the one on the spectral asymptotics for a certain Jacobi matrix.
