Oleg Safronov
The discrete spectrum in the spectral gaps of semibounded operators with 
non-signdefinite perturbations
(188K, Postscript)

ABSTRACT.   Given two selfadjoint operators $A$ and $V=V_+-V_-$, 
we study the motion of the eigenvalues of the operator 
$A(t)=A-tV$ as $t$ increases. 
Let $\alpha>0$ and let $\lambda$ be a regular point for $A$. 
We consider the quantities 
$N_+(V;\lambda,\alpha),\ N_-(V;\lambda,\alpha),\ 
N_0(V;\lambda,\alpha)$ 
defined as the number of the eigenvalues of the operator 
$A(t)$ that pass point $\lambda$ 
from the right to the left, 
from the left to the right or change the direction of 
their motion exactly at point $\lambda$, 
respectively, as $t$ increases from $0$ to $\alpha>0.$ 
 We study asymptotic characteristics of these quantities 
as $\alpha\to \infty.$ 
In the present paper we extend the 
results obtained in \cite{S2} and give new 
applications to differential operators.