New method of investigation of the Fredholm property of three-dimensional Helmholtz equation with nonlocal boundary value conditions


Mustafayeva Yelena, Aliyev Nihan




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.