一类二阶时滞方程振动性准则

Criterion for Oscillation of a Class of Second-order Delay Equations

考虑二阶时滞方程其中ｂ，ｑ，ｋ，τ为常数，ｑ０，τ＞０。方程（＊）是Ｍｉｎｏｒｓｋｙ［１］在研究船体摆动控制问题时提出的数学模型。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。

Consider Scond-order delay equations x(t) + bx(t) + qx(t - ) + lcx(t)= 0 where b, q, k, are constants, is a mathematical model raised by Minorsky [1] in studying the control problem of ship body's swaying. The author establishes a necessary and suficient condition for oscillation of Eq.(*), which is easy to verify and apply .