Geodesic
Polynomial differential systems with explicit expression
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2019), pp. 65-74 
Mouna Yahiaoui; Rachid Boukoucha. Polynomial differential systems with explicit expression. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2019), pp. 65-74. http://geodesic.mathdoc.fr/item/BASM_2019_3_a6/
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     url = {http://geodesic.mathdoc.fr/item/BASM_2019_3_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we give an explicit expression of invariant algebraic curves of multi-parameter planar polynomial differential systems of degree nine, then we prove that these systems are integrable and we introduce an explicit expression of a first integral. Moreover, we determine sufficient conditions for these systems to possess two limit cycles: one of them is algebraic and the other one is shown to be non-algebraic, explicitly given. Concrete examples exhibiting the applicability of our result are introduced.

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