Title: | Non-oscillation of second order linear self-adjoint nonhomogeneous difference equations (English) |

Author: | Parhi, N. |

Language: | English |

Journal: | Mathematica Bohemica |

ISSN: | 0862-7959 (print) |

ISSN: | 2464-7136 (online) |

Volume: | 136 |

Issue: | 3 |

Year: | 2011 |

Pages: | 241-258 |

Summary lang: | English |

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Category: | math |

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Summary: | In the paper, conditions are obtained, in terms of coefficient functions, which are necessary as well as sufficient for non-oscillation/oscillation of all solutions of self-adjoint linear homogeneous equations of the form \[ \Delta (p_{n-1}\Delta y_{n-1}) + q y_{n} =0 , \quad n\geq 1, \] where $q$ is a constant. Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of all solutions of nonlinear non-homogeneous equations of the type \[ \Delta (p_{n-1}\Delta y_{n-1}) + q_{n}g( y_{n}) = f_{n-1}, \quad n\geq 1, \] where, unlike earlier works, $f_{n}\geq 0$ or $\leq 0$ (but $\not \equiv 0)$ for large $n$. Further, these results are used to obtain sufficient conditions for non-oscillation of all solutions of forced linear third order difference equations of the form \[ y_{n+2}+ a_{n}y_{n+1}+ b_{n}y_{n}+ c_{n}y_{n-1}= g_{n-1}, \quad n\geq 1. \] (English) |

Keyword: | oscillation |

Keyword: | non-oscillation |

Keyword: | second order difference equation |

Keyword: | third order difference equation |

Keyword: | generalized zero |

MSC: | 39A06 |

MSC: | 39A10 |

MSC: | 39A12 |

MSC: | 39A21 |

idZBL: | Zbl 1249.39015 |

idMR: | MR2893974 |

DOI: | 10.21136/MB.2011.141647 |

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Date available: | 2011-09-22T14:55:17Z |

Last updated: | 2020-07-29 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/141647 |

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Reference: | [9] Parhi, N., Panda, A.: Oscillatory and non-oscillatory behaviour of solutions of difference equations of the third order.Math. Bohem. 133 (2008), 99-112. MR 2400154 |

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