某类二阶多时滞泛函微分方程的振动性

The Oscillation of Some Second-Order Functional Differential Equations with Many Delays

利用微分不等式研究了一类具有n个时滞的二阶泛函微分方程的振动解与非振动解问题,通过构造序列得到了方程具有非振动解的必要条件和振动解的充分条件;另外,对两类比较具体的泛函微分方程,采用另一种方法得到了方程一切有界解振动的充分条件.

By using the differential inequality, the oscillatory solution and nonosdllatory solution of a second-order functional differential equation with n delays has been investigated, we obtain the necesary condition for this equation has a nonoscillatory solution and some sufficient condition for that has a oscillatory solution by the functional sequence; in addition, we obtain the suffident condition which ensures that all the bounded solutions of the two specific functional differential equations are oscillatory.