On boundary problems for general differential equations, new moment problem and criteria for the solvability of Poncelet problem

The talk is devoted to research on the theory of boundary value problems for general partial differential equations and their applications. In particular, for the case of the second order a new moment problem arises and its indefiniteness is equivalent to non-uniqueness of the solution of the corresponding Dirichlet or Neumann problem. Arising connections allowed to find a new form of criterion for the solvability of the classical Poncelet problem.