NEW METHOD OF INVESTIGATION OF THE FREDHOLM PROPERTY OF THREE-DIMENSIONAL HELMHOLTZ EQUATION WITH NONLOCAL BOUNDARY VALUE CONDITIONS

Abstract

The paper is dedicated to the investigation of the Fredholm property of boundary value problems with nonlocal boundary conditions for a three-dimensional Helmholtz equation. The basic relationships giving complete system of necessary conditions for the solvability of the boundary value problem are obtained on the assumption of well-known fundamental solution of Helmholtz equation. Some of these conditions contain singularities the regularization of which cannot be done by conventional methods and is conducted by an original scheme.