【摘要】 二阶时滞方程 ｘ（ｔ）＋ａｘ（ｔ）＋ ｂｘ（ｔ）＋ｃｘ（ｔ－τ）＝ ０其中ａ，ｂ．ｃ，τ为常数，Ｃ≠０，τ＞０．方程（＊）是加藤仁［ｌ］等在研究金属切削被加工物件沿水平方向颤震振动问题时提出的数学模型。本文给出了方程（＊）所有解振动的代数判据，即参数形式的充要条件，这些条件易于检验和应用。更多还原

【Abstract】 Consider second-order delay equations x(t) + ax(t) + bx(t) +cx(t-τ) =0 (*) where a, b, c, τ are constants, c≠0, τ>0. Eq.(*) is a mathematical model raised by Kato [1] in studying mechanical oscillation. In this paper, we establish a necessary and suficient condition for oscillation of Eq.(*), which is easy to verify and to apply.更多还原