On the existence of a periodic solution of the Lienard system with impulse effect

We consider a system of Liénard differential equations with impulse effect
$$ \frac{dx}{dt}=z-F(x),\quad \frac{dz}{dt}=-g(x),\quad \text{ for}\quad x\ne 0, $$

$$ \Delta x=0,\quad \Delta z=J(z)\quad \text{ for}\quad x= 0. $$
Sufficient conditions for the existence of a periodic solution of this system are obtained.