Lunyov A. On completeness and Riesz basis property of boundary value problems for systems of ordinary differential equations

The thesis is devoted to the study of some spectral properties of the general boundary value problems (BVP) for first order system of ordinary differential equations (ODE). Some spectral properties of higher order ODE on semi-axis are also investigated. For general BVP for first order system of ODE with non-weakly regular boundary conditions, completeness property was obtained under certain potential-dependent conditions. Riesz basis property with parentheses for such BVP with a wide class of regular boundary conditions and bounded potential matrix was established. These results were used to obtain new conditions of completeness and Riesz basis property with parentheses for the dynamic generator of the general spatially non-homogeneous Timoshenko beam model with smoothness assumptions on the parameters of the model that were not treated in the previous papers. For the second order ODE, new conditions on a complex-valued potential guarantying convergence of all solutions to zero at infinity were obtained. An explicit formula for a spectral function for Dirichlet and Neumann BVP on a semiaxis for differential operator of even order with zero coefficients was obtained using the method of boundary triplets.