Предельно периодические движения при резонансе в системах, описываемых интегродифференциальными уравнениями типа Вольтерра

Motions which tend to periodic oscillations with time are considered. The critical case of a pair of pure imaginary roots is analyzed by the first Lyapunov's method for equations with analytical nonlinear parts and Lyapunov's constant g3 ¹ 0. The existence of a family of limiting periodic solutions is proved for the case when the frequency of external small perturbations coincides with the fundamental frequency of the linearized unperturbed system.