About one high-order linear equation of mixed type

We consider the question of solvability of the boundary value problem for the high-order differential equation of mixed type in the domain $Q=tx\Omega$, where $t\in (0,1)$, $x\in\Omega R^n$. We study arbitrary boundary conditions on the lateral surface of a cylinder and a rather general class of boundary conditions at upper and lower foundations of a cylinder. A peculiarity of the problem is that the coefficient of the leading derivative with respect to t in the operator of mixed type may change sign.