Spatial mixed problems and Neumann problem for the threedimensional elliptic equation with the two singular coefficients

In the present work, a spatial mixed problems and Neumann problem for a threedimensional elliptic equation with two singular coefficients are investigated. Using an "abc" method, the uniqueness for the solution of the mixed problems is proved. It is shown that the solution to the Neumann problem is not unique and each solution differs from the other with a constant. Applying a method of Green’s functions, we are able to find the solution of the problem in an explicit form, in finding which the properties of the Appel and Gauss hypergeometric functions are essentially used.