Consider the delay difference equation with continuous time of the form [x(t)-x(t-1)+sum_{i=1}^mP_i(t)x(t-k_i(t))=0,qquad tge t_0,] where $P_icolon[t_0,infty)mapstomathbb{R}$, $k_icolon[t_0,infty)mapsto {2,3,4,dots}$ and $lim_{toinfty}(t-k_i(t))=infty$, for $i=1,2,dots,m$. We introduce the generalized characteristic equation and its importance in oscillation of all solutions of the considered difference equations. Some results for the existence of positive solutions of considered difference equations are presented as the application of the generalized characteristic equation.
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机译：考虑连续时间形式为 [x（t）-x（t-1）+ sum_ {i = 1} ^ mP_i（t）x（t-k_i（t））= 0，的延迟差分方程qquad t ge t_0，]其中$ P_i 冒号[t_0， infty） mapsto mathbb {R} $，$ k_i colon [t_0， infty） mapsto {2,3,4， dots } $和$ lim_ {t to infty}（t-k_i（t））= infty $，其中$ i = 1,2， dots，m $。我们介绍了广义特征方程及其在考虑的差分方程所有解的振动中的重要性。给出了考虑的差分方程正解存在性的一些结果，作为广义特征方程的应用。
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