一阶非线性多时滞微分方程的振动性

Linearized Oscillation of First Order Nonlinearity Multi-Delay Differential Equation

考虑一阶非线性多时滞微分方程x′(t)=f(t,x(t-r_1),x(t-r_2),…,x(t-r_n)),利用其线性近似方程x′(t)=∑i=1nD_(i+1)f(t,0,…,0)x(t-r_i)的振动性,给出了方程解振动的一个充分条件,所得结果推广了文献[5]的相关结果.

Consider the first order nonlinear multi-delay differential equation x＇[t） = f（t, x（t - rl）, x（t - r2）,···, x（t - rn））. By using the oscillation of its linearized equation x＇（t） = ∑i^n=Di＋lf（t, 0,··· , O）x（t - ri）, a suffieent condition for oscillation of the equation is obtained, which generalized from the results of [5].