Authors: | Stević, Stevo |

Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts |

Title: | Asymptotic behavior of solutions of a nonlinear difference equation with continuous argument |

Journal: | Ukrainian Mathematical Journal |

Volume: | 56 |

Issue: | 8 |

First page: | 1300 |

Last page: | 1307 |

Issue Date: | 1-Jan-2004 |

ISSN: | 0041-5995 |

DOI: | 10.1007/s11253-005-0058-1 |

Abstract: | We consider the difference equation with continuous argument x(t + 2) - 2λ x(t + 1) + λ 2 x(t) = f(t,x(t)), where λ > 0, t [0, ∞), and f: [0, ∞) × R → R. Conditions for the existence and uniqueness of continuous asymptotically periodic solutions of this equation are given. We also prove the following result: Let x(t) be a real continuous function such that lim (x(t + 2) - (1 -α)x(t + 1) - αx(t)) = 0 for some α R. Then it always follows from the boundedness of x(t) that lim(x(t + 1) - x(t)) = 0 t → ∞ if and only if α R {1}. |

Publisher: | Springer Link |

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