## Abstract

In this paper, we prove that Wright's equation y^{′}(t)=−αy(t−1){1+y(t)} has a unique slowly oscillating periodic solution (SOPS) for all parameter values α∈[1.9,6.0], up to time translation. Our proof is based on the same strategy employed earlier by Xie [27]; show that every SOPS is asymptotically stable. We first introduce a branch and bound algorithm to control all SOPS using bounding functions at all parameter values α∈[1.9,6.0]. Once the bounding functions are constructed, we then control the Floquet multipliers of all possible SOPS by solving rigorously an eigenvalue problem, again using a formulation introduced by Xie. Using these two main steps, we prove that all SOPS of Wright's equation are asymptotically stable for α∈[1.9,6.0], and the proof follows. This result is a step toward the proof of the Jones’ Conjecture formulated in 1962.

Original language | English (US) |
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Pages (from-to) | 7263-7286 |

Number of pages | 24 |

Journal | Journal of Differential Equations |

Volume | 263 |

Issue number | 11 |

DOIs | |

State | Published - Dec 5 2017 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

## Keywords

- Branch and bound
- Computer-assisted proofs
- Delay differential equations
- Jones's Conjecture
- Wright's equation