On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems

In this paper elliptic problems in exterior domains polynomially depending on a spectral parameter $k$ are considered. These problems are obtained from a mixed problem for hyperbolic equations by substituting $k$ for $id/dt$. For such elliptic problems analytic properties of the resolvent are studied in the neighborhood of the point $k=0$, which permits, for the corresponding nonstationary problem, a complete asymptotic expansion of solutions as $t\to\infty$.
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