Asymptotics of the eigenvalues of approximating differential equations with $\delta$-different coefficients

The overall objective is to describe the behavior of the eigenvalues of approximating operators and figuring out how to limit one turns one's own importance. Earlier we have done the following: built approximation expression $L_{0}u = -\Delta u+a(\varepsilon)\delta u = f$ operators of finite rank; explicit form approximating the resolvent family; resolutions and found the limit cases of resonance highlighted. In this article, we will continue to address this problem and set out a step associated with the description of the spectrum constructed limit operators and study the behavior of the eigenvalues of approximating operators, using Newton's diagram method. As a result of eigenvalues of the operator were found.