In this article we obtain sufficient conditions for the oscillation of all solutions of the higher-order delay difference equation Δ m(yn− ∑ j=1kpnjyn− mj)+vnG(yσ (n))− unH(yα (n))=fn,$$\begin{array}{} \displaystyle \Delta^{m}\big(y_n-\sum_{j=1}^k p_n^j y_{n-m_j}\big) + v_nG(y_{\sigma(n)})-u_nH(y_{\alpha(n)})=f_n\,, \end{array}$$ where m is a positive integer and Δ x n = x n +1 − x n . Also we obtain necessary conditions for a particular case of the above equation. We illustrate our results with examples for which it seems no result in the literature can be applied.

中文翻译：

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Δm以下变时滞的高阶中立型时滞差分方程的振动性和渐近性

在本文中，我们为高阶延迟差分方程Δm（yn- ∑ j = 1kpnjyn- mj）+ vnG（yσ（n））-unH（yα（n））=的所有解的振动提供了充分的条件。 fn，$$ \ begin {array} {} \ displaystyle \ Delta ^ {m} \ big（y_n- \ sum_ {j = 1} ^ k p_n ^ j y_ {n-m_j} \ big）+ v_nG（y_ { \ sigma（n）}）-u_nH（y _ {\ alpha（n）}）= f_n \，\ end {array} $$，其中m为正整数，Δxn = xn +1 − xn。我们还为上述方程式的特定情况获得了必要条件。我们用例子说明我们的结果，在文献中似乎没有结果可以应用。