  We consider singular perturbed eigenvalue problem for Laplace operator in a
two-dimensional domain. In the boundary we select a set depending on a
character small parameter and consisting of a great number of small disjoint
parts. On this set the Dirichlet boundary condition is imposed while on the
rest part of the boundary we impose the Neumann condition. For the case of
homogenized Neumann or Robin boundary value problem we obtain highly weak
restrictions for distribution and lengths of boundary Dirichlet parts of the
boundary under those we manage to get the leading terms of asymptotics
expansions for perturbed eigenelements. We provide explicit formulae for these
terms. Under weaker assumptions we estimate the degrees of convergence for
perturbed eigenvalues.
