Oscillatory And Asymptotic Behaviors Of Higher-order Nonlinear Differential Equations With Impulses

In this paper, we study the oscillatory and asymptotic behaviors of higher-order nonlinear differential equations with impulses. In the first part, we devote to investigate a class of the even-order nonlinear impulsive differential equations, and derive four oscillation criteria. Next, as the application of the above mentional oscillation criteria, we also get four theorems for enssuring oscillation of every solution of a class of even-order nonlinear impulsive differential equations with damping. In the second part, we investigate the oscillatory and asymptotic behaviors of a class of odd-order nonlinear differential equations with impulses, and obtain three critera that enssure every solution is either oscillatory or (nonoscillatory and) zero convergent.In both of the above two parts, our theorems are either new or improve several recent results in the literature. In addition, we provide several examples to show that impulses play an important role in the oscillatory and asymptotic behaviors of equations.