On a boundary problem with Neumann’s condition for 3D singular elliptic equations

The present work is devoted to the studying of a boundary-value problem with Neumann’s condition for three-dimensional elliptic equation with singular coefficients. The main result is a proof of the unique solvability of the problem considered. An energy integral method and a Green’s function method were used as the main tools in the proof of the main result. The unique solution is found in an explicit form, which contains Appel’s hypergeometric functions.