Abstract
AbstractIn this article we obtain sufficient conditions for the oscillation of all solutions of the higher-order delay difference equationΔm(yn−∑j=1kpnjyn−mj)+vnG(yσ(n))−unH(yα(n))=fn,$$\begin{array}{} \displaystyle \Delta^{m}\big(y_n-\sum_{j=1}^k p_n^j y_{n-m_j}\big) + v_nG(y_{\sigma(n)})-u_nH(y_{\alpha(n)})=f_n\,, \end{array}$$wheremis a positive integer and Δxn=xn+1−xn. 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.
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