Polynomial differential systems with hyperbolic algebraic limit cycles

Benyoucef, Salah, Department of Mathematics, Faculty of Sciences, University Setif 1, Algeria.

Electron. J. Qual. Theory Differ. Equ. 2020, No. 34, 1-7. DOI: https://doi.org/10.14232/ejqtde.2020.1.34

Communicated by  Villari, Gabriele

Received on 2020-03-30 Appeared on 2020-05-29

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Abstract: For a given algebraic curve of degree $n$, we exhibit differential systems of degree greater than or equal $n$, by introducing functions which are solutions of certain partial differential equations. These systems admit precisely the bounded components of the curve as limit cycles.

Keywords: sixteenth problem of Hilbert, planar differential system, invariant curve, periodic solution, hyperbolic limit cycle

Mathematics Subject Classification: 34C25, 34C05, 34C07

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