## Abstract

We study a bifurcation from the zero solution of the differential equation ẍ + x^{p}/^{q} = 0, where p > q > 1 are odd coprime numbers, under periodic (in particular, time-invariant) perturbations depending on a small positive parameter ε. The motion separation method is used to derive the bifurcation equation. To each positive root of this equation, there corresponds an invariant two-dimensional torus (a closed trajectory in the time-invariant case) shrinking to the equilibrium position x = 0 as ε → 0. The proofs use methods of the Krylov-Bogolyubov theory to study time-periodic perturbations and the implicit function theorem in the case of time-invari ant perturbations.

Original language | English |
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Pages (from-to) | 753-757 |

Journal | Differential Equations |

Volume | 55 |

Issue number | 6 |

Early online date | 15 Jul 2019 |

DOIs | |

State | Published - 2019 |

## Scopus subject areas

- Analysis
- Mathematics(all)