Title: | Existence and Stability of Periodic Solutions for Nonlinear Neutral Differential Equations with Variable Delay Using Fixed Point Technique (English) |

Author: | MESMOULI, Mouataz Billah |

Author: | Ardjouni, Abdelouaheb |

Author: | Djoudi, Ahcene |

Language: | English |

Journal: | Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |

ISSN: | 0231-9721 |

Volume: | 54 |

Issue: | 1 |

Year: | 2015 |

Pages: | 95-108 |

Summary lang: | English |

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Category: | math |

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Summary: | Our paper deals with the following nonlinear neutral differential equation with variable delay \[ \frac{d}{dt}Du_{t}(t) =p (t)-a(t)u (t)-a(t) g(u(t-\tau (t))) -h (u(t) ,u (t-\tau (t))) . \] By using Krasnoselskii’s fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. A sufficient condition is established for the positivity of the above equation. Stability results of this equation are analyzed. Our results extend and complement some results obtained in the work [Yuan, Y., Guo, Z.: On the existence and stability of periodic solutions for a nonlinear neutral functional differential equation Abstract and Applied Analysis 2013, ID 175479 (2013), 1–8.]. (English) |

Keyword: | Fixed point theorem |

Keyword: | contraction |

Keyword: | compactness |

Keyword: | neutral differential equation |

Keyword: | integral equation |

Keyword: | periodic solution |

Keyword: | positive solution |

Keyword: | stability |

MSC: | 34K20 |

MSC: | 34K30 |

MSC: | 34K40 |

MSC: | 45D05 |

MSC: | 45J05 |

MSC: | 47H10 |

idZBL: | Zbl 1347.34108 |

idMR: | MR3468603 |

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Date available: | 2015-09-01T09:02:29Z |

Last updated: | 2018-01-10 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/144370 |

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Reference: | [14] Zhang, B.: Fixed points and stability in differential equations with variable delays. Nonlinear Anal. 63 (2005), 233–242. Zbl 1159.34348, 10.1016/j.na.2005.02.081 |

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