On the Non-Uniqueness of Solutions to Nonlinear Integral Equations of Antenna Synthesis Theory

The study of the problem of non-uniqueness of the solutions to a nonlinear integral equation arising in the antenna synthesis theory is carried out. The application of methods of solving the two-parameter spectral problems makes it possible to find a set of points of perspective branching (bifurcation) to solutions in the form of spectral curves or surfaces in a fixed area. The new branched solutions are complex, and they are more effective in sense of respective functional than the initial real solutions.