On singularly perturbed elliptic spectral problems.

We consider a boundary value problem for an elliptic operator of order 2 in a bounded domain with boundary condition depending on a parameter. We study the behaviour of eigenvalues and eigenfunctions for large values of the parameter and establish a dependence of coefficients in asymptotic expansions on the domain. We also investigate spectral properties of the elliptic operators for some classes of unbounded domains.