Homogenization of spectral problems with singular perturbation of the Steklov condition

We consider spectral problems with Dirichlet- and Steklov-type conditions on alternating small pieces of the boundary. We study the behaviour of the eigenfunctions of such problems as the small parameter (describing the size of the boundary microstructure) tends to zero. Using general methods of Oleinik, Yosifian and Shamaev, we give bounds for the deviation of these eigenfunctions from those of the limiting problem in various cases.