  A fundamental result that characterizes elliptic-hyperbolic equations of
Tricomi type, the uniqueness of classical solutions to the open Dirichlet
problem, is extended to a large class of elliptic-hyperbolic equations of
Keldysh type. The result implies the non-existence of classical solutions to
the closed Dirichlet problem for this class of equations. A uniqueness theorem
is also proven for a mixed Dirichlet-Neumann problem. A generalized uniqueness
theorem for the adjoint operator leads to the existence of distribution
solutions to the closed Dirichlet problem in a special case.
