On a perturbation of the poles of scattering matrix for varying baundary condition

It is considered the behavior of the poles $z_n(\varepsilon)$, $n=1,2,\dots$ of scattering matrix of the operator $l_\varepsilon u=-\Delta u(x), x\in\Omega, \displaystyle\varepsilon\frac{\partial u}{\partial n}+\sigma(x)u|_{\partial\Omega}$ for $\varepsilon\to0$. It is proved that $|z_n(\varepsilon)-z_n|=O(\varepsilon^{\frac1{2q_n}})$ where $q_n$ is the order of pole $z_n$ of scattering matrix of the operator $l_0u=-\Delta u, u|_{\partial\Omega}=0$.