Vibrating systems with heavy soft inclusions (in Ukrainian)

The Neumann spectral problem for an elliptic operator of the second order with singularly perturbed coefficients is considered. The asymptotic behavior of eigenvalues and eigenfunctions is studied. The problem describes the eigenmodes of a composite material with a finite number of heavy and soft inclusions. The number-by-number convergence of the eigenvalues and the corresponding eigenspaces is established. The limit eigenvalue problem involves a non-local boundary condition which arises from the non trivial coupling of the inclusions.