一类二阶非线性变时滞微分方程的振动准则

Oscillatory Criterion of a Kind of Second-order Nonlinear Variable Delay Differential Equation with Variable Coefficient

研究二阶非线性变时滞微分方程x″(t)+p(t)f(x(g(t)))=0,对振动因子p(t)变符号的情况讨论了方程的振动性,通过两个已有引理得到了方程振动的两个充分条件.所得结论推广了原有的二阶非线性微分方程与变时滞微分方程当系数不变号时的振动性结论,完善了具变符号振动因子的二阶非线性变时滞微分方程的研究.

This paper studies the oscillation of second-order variable delay differential equation x″（t） ＋ p（t）f（x（g（t））） = 0. By using two lemmas, we gain two sufficient conditions for the oscillation of all solutions of the equation with variable coefficient p（t）. We generalize the oscillation results of second-order nonlinear differential equation and variable delay differential equation with invariable coefficient. We also develop the oscillation results of second-order nonlinear variable delay differential equation with variable coefficient.