A brief overview of the works of the author and his co-authors on the application of nonlinear analysis methods for solving the nonlinear inverse problems (synthesis problems) for optimizing the different types of radiating systems are presented in the paper. The synthesis problem are formulated in variational statements and further they are reduced to research and numerical solution of nonlinear integral equations of Hammerstein type. The existence theorems are proof, the investigation methods

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... of nonuniqueness problem of solutions and numerical algorithms of finding the optimal solutions are proved.