On the existence of solutions of synthesis problems for radiating systems in terms of a prescribed amplitude directional pattern

Abstract

We study two variational formulations for nonlinear inverse problems applied to the synthesis of radiating systems, and we derive nonlinear operator equations that follow from the necessary condition for the functional to have a minimum. On the basis of the properties of these functionals we prove theorems and exhibit an existence domain for solutions of this class of problems. Using the example of a linear grid, we exhibit the transition from the variational formulation of a problem to nonlinear integral equations of Hammerstein type.