Voytitsky V. Boundary value problems with spectral parameter in equations and boundary conditions

The thesis is devoted to study of new spectral boundary value and transmission problems with spectral parameter in equations and boundary conditions. By using theory of operators acting in Hilbert space we establish basic properties for systems of eigen elements and qualitative properties of spectrums for linearized Stefan problems with classical and modified boundary conditions. Analogous results are obtained for the abstract spectral problems which can be formulated using operators from abstract Green's formula. At first time we considered the spectral properties of mathematical model of small motions and normal oscillations of a heavy super fluid in an open vessel.