Geodesic
On the existence of a periodic solution of the Lienard system with impulse effect
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 1, pp. 79-87

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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.
Keywords: systems of differential equations with impulse effect, Liénard system, limit cycle. 
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A. O. Ignatyev. On the existence of a periodic solution of the Lienard system with impulse effect. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 1, pp. 79-87. http://geodesic.mathdoc.fr/item/TIMM_2021_27_1_a7/