某类系数变号的二阶非线性变时滞微分方程的振动性

Oscillation of Second-order Nonlinear Variable Delay Differential Equation with Variable Coefficient

研究了二阶非线性变时滞微分方程x″(t)+p(t)f(x(g(t)))=0的振动性,对振动因子p(t)变号的情况,给出了两个重要的引理,并得到方程振动的一个充分性定理.所得结论推广了二阶非线性变时滞微分方程当系数不变号时原有的振动性结论.

This paper studies the oscillation of a kind of second-order variable delay differential equation x″（t） ＋ p（t）f（x（g（t））） = 0. Two important lemmas and a sufficient condition for the oscillation of all solutions of the equation with variable coefficient p（t） are obtained. We generalize the results of second-order nonlinear differential equation and variable delay differential equation with invariable coefficient.