On periodic solutions of autonomous systems
The author considers the periodic problem of autonomous dynamical systems described by ordinary differential equations with phase and integral restrictions as a boundary-value problem with restrictions. By introducing a fictitious control, the boundary-value problem is transformed into a control problem for dynamical systems with phase and integral restrictions. The control problem is solved by reducing it to an integral Fredholm equation of the first kind. The author establishes necessary and sufficient conditions for the existence of periodic solutions and propose an algorithm for finding periodic solution according to the limit points of the minimizing sequences.
scientific article; zbMATH DE number 6854257
scientific article