Forced resonant oscillations of nonlinear autonomous system in equilibrium neighborhood

Consideration was given to existence and stability of oscillations in the case of resonance where in the neighborhood of equilibrium the autonomous nonlinear system is subjected to periodic perturbations. For each of the probable cases where the equilibrium is surrounded or not by a family of periodic oscillations, established were the sufficient conditions solving the problem. The amplitudes of the resonant oscillations were estimated in terms of the small parameter.