  Finiteness of the point spectrum of linear operators acting in a Banach space
is investigated from point of view of perturbation theory. In the first part of
the paper we present an abstract result based on analytical continuation of the
resolvent function through continuous spectrum. In the second part, the
abstract result is applied to differential operators which can be represented
as a differential operator with periodic coefficients perturbed by an arbitrary
subordinated differential operator.
