## Abstract

In this paper we are dealing with the oscillatory and asymptotic behaviour of solutions of second order nonlinear difference equations of the form Δ(r_{n}Δx_{n}) + f(n, x_{n}) = 0, n ∈ N(n_{0}). (1) We obtain the following results. (a) If ∑^{+∞}_{k = n0} (l/r_{k}) < + ∞ any nonoscillatory solution of (1) must belong to one of the following four types: K^{β}_{α}, K^{∞}_{α}, K^{β}_{0}, K^{∞}_{0}. (b) If ∑^{+∞}_{k = n0} (l/r_{k}) = + ∞ any nonoscillatory solution of (1) must belong to one of the following three types: K^{0}_{α}, K^{β}_{∞}, K^{0}_{∞}. (c) Necessary and sufficient conditions for (1) to have a nonoscillatory solution which belongs to K^{β}_{α}, K_{α}, K^{β}_{0}, K^{0}_{α}, or K^{β}_{∞} are given depending on whether f is a superlinear or sublinear function. All these results include and improve B. Szmanda′s results in Bull. Polish Acad. Sci. Math.34, Nos. 3-4, 1986, 133-141.

Original language | English |
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Pages (from-to) | 482-498 |

Number of pages | 17 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 175 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1993 |

Externally published | Yes |