On Mitropol'skii Yu.A.'s Theorem on Periodic Solutions of Systems of Nonlinear Differential Equations with Non-Differentiable Right-Hand-Sides

TL;DR

This paper extends Bogolyubov's second theorem to Lipschitz continuous systems, broadening the applicability of the theorem to non-differentiable cases.

Contribution

It generalizes the smooth second Bogolyubov's theorem to systems with Lipschitz continuous right-hand sides, which are not necessarily differentiable.

Findings

The theorem is successfully extended to Lipschitz systems.

Conditions for the existence of periodic solutions are established.

The generalization broadens the scope of the original theorem.

Abstract

The smooth second Bogolyubov's theorem is generalized for Lipschitz systems.