Application of multidimensional residues theory to determining number of solutions of transcendental equation systems arisen in phase optimization problems

The subject of investigation is to determine the number of solutions to the system of transcendental equations related to a class of nonlinear integral equations of Hammerstein type with separated argument (phase) of unknown function. Such systems have arisen particularly in the phase optimization problems. The numerical algorithm is constructed and demonstrated on an example of equation of two complex unknowns.