About completeness of products of functions, initiated by singular differential equations

In this article we introduced the completeness theorem for special vector-functions, initiated by products of Weil solutions of forth order differential equation and its derivatives on the halfine. We prove that such nonlinear combinations of Weil solutions and its derivatives form the linear subspace of solutions, which decrease to infinity, of linear singular Kamke-type differential system. Then we construct and investigate Green function of corresponding singular boundary problem for the operator-pencils, which determine Kamke-type differential system.With help of analytic and asymptotic properties of Green function, methods of spectral theory of operators and theory of analytic functions we prove the required completeness theorem.