Types Of Differential Equations Of State

This paper is composed of two chapters. We study the oscillation of two types of differential equations and the periodic solutions of some type of differential equation and acquires a series of conclusions. Some of those conclusions improve or extend the related results in the literatures.Chapter 1 focused on the oscillation of some second order nonlinear differential equation and some even order delay differential equation with damping. By using the new methods of Riccati transformation and weighted average, sufficient conditions are obtained.Chapter 2 concerns the existence of periodic solutions of a class of impulsive differential equations. Based on the coincidence degree and its related continuation theorem, sufficient criterion is established.