Periodic solutions of a class of nonlinear systems of ordinary differential equations (Q2387917)

The existence of periodic solutions of second-order differential equations has been studied permanently in the 20th century. In particular, in the last ten years, some studies were concentrated on the existence of multiple periodic solutions. The paper is also in this direction. It is based on using Lagrange multipliers in combination with the fibering method. This is an idea suggested by S. I. Pokhodzaev which further was employed many times for the investigation of nonlinear boundary value problems. In the paper under review, a special class of nonlinear systems of differential equations is considered. Introducing a variety of assumptions related to the different cases of differential equations, the existence of periodic solutions is proved. At the end, several examples are shown.