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In this paper we study the existence, uniqueness and asymptotic stability ofthe periodic solutions for a Lipschitz system with a small right hand side.Classical hypotheses in the periodic case of second Bogolyubov's theorem implyour ones. By means of the results established we construct the curves ofdependence of the amplitude of asymptotically stable $2\pi$--periodic solutionsof the nonsmooth van der Pol oscillator on the detuning parameter and theamplitude of the perturbation. After, we compare the resonance curves obtained,with the resonance curves of the classical van der Pol oscillator which werefirst constructed by Andronov and Witt.

Asymptotic stability of periodic solutions for nonsmooth differential equations with application to the nonsmooth van der Pol oscillator