### Abstract

We prove the existence of at most three limit cycles for a family of planar polynomial differential equations. Moreover we show that this upper bound is sharp. The key point in our approach is that the differential equations of this family can be transformed into Abel differential equations. © 2013 University of Houston.

Original language | English |
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Pages (from-to) | 191-203 |

Journal | Houston Journal of Mathematics |

Volume | 39 |

Issue number | 1 |

Publication status | Published - 15 Aug 2013 |

### Keywords

- Abel equation
- Limit cycle
- Polynomial differential system
- Riccati equation

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## Cite this

Gasull, A., & Zhao, Y. (2013). On a family of polynomial differential equations having at most three limit cycles.

*Houston Journal of Mathematics*,*39*(1), 191-203.