The Dirichlet problem for an equation of mixed elliptic-hyperbolic type with variable potential
We study the Dirichlet problem for an equation of mixed elliptic-hyperbolic type with variable potential in the rectangular area. We establish a criterion of the uniqueness of a solution to this problem. The uniqueness of a solution is proved on the basis of the completeness of systems of functions corresponding to one-dimensional spectral problem. Solution was constructed as a sum of series on the systems of eigenfunctions. The existence is proved under certain conditions upon the ratio of the rectangle sides of hyperbolic part of the equation, upon the boundary functions and function of potential.