In the variational argument, a nonlinear synthesis problem of antennas according to the specified energetic radiation pattern (RP) is considered, resulting in the possibility of taking into account an additional constraint to the synthesised energetic RP. The synthesis problem consists of finding such antenna currents, which generates the RP with the best approximation to the one given. The groups of nonlinear problems for which the non-uniqueness of solutions, their branching and bifurcation are characteristic, emerge in such a formulation. Solution properties depend on the electrical size of the antenna device and the energetic RP prescribed. For solving the synthesis problem, effective numerical methods are developed and implemented. Computational outcomes check the feasibility of the suggested solution. The existence of several types of different solutions, from a practical point of view, that generate the same or similar energetic RP, allows us to choose the solution that has a simpler implementation of engineering.

**Author(s) Details**

**Prof. M. I. Andriychuk
**Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, Lviv, Ukraine.

**Prof. B. M. Podlevskyi
**Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, Lviv, Ukraine.

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