On the existence of discontinuous periodic solutions for a class of Liénard systems with impulses

In this paper, we investigate the existence of discontinuous periodic solutions for a class of Liénard systems with state impulses, whose solutions are interrupted by abrupt changes of state. By employing Poincaré mapping method, a criterion for the existence of at least one discontinuous periodic solution in the impulsive Liénard systems is established. Finally, we give an example to illustrate the effectiveness of our result, and the corresponding numerical simulation is presented to show that there is a good agreement between our theoretical result with the computer numerical analysis.