We consider a system of Li$\acute{\mathrm{e}}$nard 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, Lienard system, limit cycle
Received December 8, 2020
Revised December 25, 2020
Accepted January 11, 2021
Alexander Olegovich Ignatyev, Dr. Phys.-Math. Sci., Prof., Institute of Applied Mathematics and Mechanics, Donetsk, 83114 Ukraine, e-mail: aoignat@mail.ru
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Cite this article as: A.O. Ignatyev. On the existence of a periodic solution of the Li$\acute{\mathrm{e}}$nard system with impulse effect, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 1, pp. 79–87.