Protsakh L. Nonlinear two-parameter spectral problems in synthesis theory of antennas with flat radiating aperture

The thesis is devoted to the technique of investigation the problem of nonuniqueness and branching of solutions of two-dimensional nonlinear integral equations of Hammerstein type arising in the problems of antenna synthesis with a flat radiating aperture and plane antenna arrays. The theorems of solutions existence are proved. Numerical method (the implicit function method) for solving the nonlinear two-parameter spectral problems of finding the branching lines of solutions is proposed. Analytical and numerical researching of branching solutions for nonlinear synthesis equations dependent on changes in values of aperture parameters is realized. Algorithms and software are developed, the series of computational experiments are realized, the advantages of branched complex solutions in comparison with the previously known in-phase solutions are shown. The application of implicit functions method to the solution of nonlinear two-parameter spectral problems for n-order ordinary differential equations with nonlinear occurrence of spectral parameters in the equation's coefficients and boundary conditions is shown. The implicit functions method is extended to the solution of two-parameter linear spectral problems for matrix, differential and integral operators.