Finding the Set of Branching Points of a Nonlinear Integral Equation Arising in the Synthesis Problem by a Given Power Directivity Pattern

In the synthesis problem of a plane equidistant antenna array according to the given requirements to a power directivity pattern, a nonlinear integral equation is obtained, which has a non-unique solution. One of them is trivial, from which at certain electrodynamic parameters other solutions can branch off. In the process of finding the branching curves of the solutions of the integral equation, two-parameter eigenvalue problems with spectral parameters (electrodynamic parameters) that are contained non-linearly in the kernel of the linearized integral operator are arisen. A numerical algorithm for finding eigenvalues is considered for such problems. The numerical examples are given.