On a Dirichlet problem for one improperly elliptic equation

The Dirichlet problem for sixth-order improperly elliptic equation is considered. The functional class of boundary functions, where this problem is normally solvable is determined. If the roots of the characteristic equation satisfy some conditions, the number of linearly independent solutions of the homogeneous problem and the number of linearly independent solvability conditions of the inhomogeneous problem are determined. Solutions of the homogeneous problem and solvability conditions of the inhomogeneous problem are obtained in explicit form.