Carletti Timoteo and Villari Gabriele:
*Existence of limit cycles for some generalisation of the Liénard equations : the relativistic and the prescribed curvature cases.*
(2020)

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## Abstract

We study the problem of existence of periodic solutions for some generalisations of the relativistic Liénard equation d dt x˙ 1 − x˙ 2 f(x, x˙)x˙ + g(x) = 0 , and the prescribed curvature Liénard equation d dt x˙ 1 + x˙ 2 f(x, x˙)x˙ + g(x) = 0 , where the damping function depends both on the position and the velocity. In the associated phase-plane this corresponds to a term of the form f(x, y) instead of the standard dependence on x alone. By controlling the continuability of the solutions, we are able to prove the existence of at least a limit cycle in the associated phase-plane for both cases, moreover we provide results with a prefixed arbitrary number of limit cycles. Some examples are given to show the applicability of these results.

Item Type: | Journal |
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Publication full: | Electronic journal of qualitative theory of differential equations |

Date: | 2020 |

Number: | 2 |

ISSN: | 1417-3875 |

DOI: | 10.14232/ejqtde.2020.1.2 |

Uncontrolled Keywords: | Liénard egyenlet, Differenciaegyenlet |

Additional Information: | Bibliogr.: p. 14-15. ; összefoglalás angol nyelven |

Date Deposited: | 2020. Jan. 23. 11:02 |

Last Modified: | 2021. Oct. 20. 13:52 |

URI: | http://acta.bibl.u-szeged.hu/id/eprint/66420 |

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