On Yu.A. Mitropol'skii's theorem on periodic solutions of systems of nonlinear differential equations with nondifferentiable right-hand sides

A study was conducted to investigate the existence, uniqueness, and asymptotic stability of Mitropol'skii's theorem on periodic solutions of systems of nonlinear differential equations, with nondifferentiable right-hand sides. It is essential to study MAtropol'skii's theorem, as it is noticed that some applications require the generalization of Bogolyubov's second theorem for perturbations, satisfying the Lipschitz conditions. The study also revealed that Mitropol'skii's theorem was generalized and analogues of his uniqueness result from equations with monotone nonlinearities.