ON A BOUNDARY VALUE PROBLEM FOR AN ELLIPTIC-TYPE EQUATION WITH THREE SINGULAR COEFFICIENTS IN A DOMAIN BOUNDED BY TWO PLANES IN THE FIRST OCTANT

The paper investigates a Dirichlet-type boundary value problem for a three-dimensional elliptic equation with three singular coefficients in a domain bounded by two parallel planes in the first octant. The unique solvability of the stated problem in the class of regular solutions is established. The uniqueness of a solution is proved using the method of energy integrals. To prove the existence of a solution, the Hankel integral transform method is employed.