On an inverse boundary value problem for the second-order elliptic equation with integral condition of the second kind

An inverse problem for the elliptic equation of the second order with periodical boundary conditions is investigated. The definition of a classical solution of the problem is introduced. The essence of the problem is that together with the solution it is required to determine the unknown coefficient. The problem is considered in a rectangular domain. To investigate the solvability of the inverse problem, the conversion from the original problem to the some direct auxiliary problem with trivial boundary conditions is realized. Using the principle of condensed mappings, the existence and uniqueness of the solution of the auxiliary problem are proved. The existence and uniqueness of the classical solution of the original problem are also proved.