Two non algebraic limit cycles of a class of polynomial differential systems with non-elementary equilibrium point (Q2068682)

The paper deals with polynomial differential systems of degree \(6k+1\), \(k\in\mathbb{N}^\ast\), with a non-elementary singular point. For this class of systems, the authors obtain some conditions on the parameters of the system in order to prove the existence of either two algebraic limit cycles or two non-algebraic limit cycles. Classical techniques of the Darboux theory are applied to obtain the main result of the paper. The authors also present some examples.