一类奇数阶非线性脉冲微分方程的振动性与渐近性

Oscillatory and Asymptotic Behaviors of A Class of Odd-order Nonlinear Differential Equations with Impulses

研究了一类奇数阶非线性脉冲微分方程解的振动和渐近性态.应用脉冲微分不等式和Ricatti变换,得到这类奇数阶非线性脉冲微分方程或者振动,或者渐近的若干充分性判定定理.

In this article,we investigate the oscillatory and asymptotic behaviors of a class of odd-order nonlinear differential equations with impulses.Using impulsive differential inequality and Ricatti transform,we obtain three critera that ensure every solution either oscillatory or（nonoscillatory and） zero convergent.In addition,we provide several examples to show that impulses play an important role in the oscillatory and asymptotic behaviors of equations.