多个变时滞二阶中立型微分方程解的零点分布

The Distribution of Zeros of Solutions of Second-order Neutral Differential Equations with Variable Delays

对多个变时滞二阶非线性中立型微分方程的零点分布进行了分析,通过泰勒公式展开,对二阶微分方程实施降维处理,构建其与对应一阶微分不等式间的联系,非线性方程线性化处理,进而对方程振动解的相邻零点间的距离进行了估计,推广了已有的一些研究结果。

An Estimation is established for the distance between adjacent zeros of the solutions of the nonlinear neutral differential equations with variable delays.Through the expansion of Taylor formula,the dimension of the second-order differential equation is reduced,and the relation between the second-order differential equation and the corresponding first-order differential inequality is constructed.The non-linear problem is converted into linear ones.Furthermore,the distance between adjacent zeros of the vibration solution of the equation is estimated.a lot of known results are generalized and improved.