Vragov Boundary Value Problem for a High Order Equation of Mixed-Composite Type

Using the nonstationary Galerkin method and the regularization method, the author proves the existence and uniqueness of the regular solution of one particular case of the Vragov problem for a high order equation of mixed-composite type, under the certain conditions on the coefficients and the right side of the equation. The leading coefficient of an equation can arbitrarily change its sign within cylindrical domain. It has the constant sign on the bases of cylinder. The eigenfunctions of the spectral problem for a Laplace equation are basic functions. Global a priory estimates for approximate solutions are proved. Upon them the error estimate of the approximate solutions with respect to the exact solution is obtained and expressed in terms of the regularization parameter and the eigenvalues of the above spectral problem.