Stability of autoresonance models under perturbations that are bounded in the mean

The paper is devoted to investigating the stability of growing solutions of nonlinear equations related to the autoresonance phenomenon. The stability of these solutions under persistent perturbations is analyzed. A class of perturbations is introduced, and its properties that provide the stability of autoresonance are described. The argument is based on the existence on the Lyapunov function of the unperturbed systems.