一类具变号系数的二阶非线性变时滞微分方程的振动性

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

研究一类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)可变符号的情况,通过两个引理,得出了方程振动的两个充分性定理.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的振动性结论.

This paper studies the oscillation of one kind 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.