Oscillation Of Some Impulsive Neutral Differential Equations

In this thesis,we study the oscillation criteria of some impulsive neutral differential equations.The thesis consists of five parts.In Chapter 1,the background,history and definitions of the neutral differential equation with impulses and the main results of this work are stated.In Chapter 2,we study the impulsive neutral differential equation with positive and negative coefficients.We get the oscillation criteria of this equation at first,and then provide two examples to illustrate the results of this paper.In Chapter 3,we consider the oscillation of the euler-neutral differential equation with impulses.On the basis of last Chapter,we make a special for the method.Thus,the oscillation criteria of the impulsive neutral differential equation with euler form is established.As the corollary,we can obtain an example.In Chapter 4,we further investigate the oscillation of the second-order impulsive neutral differential equation with positive and negative coefficients.We get all the solutions of second-order impulsive differential equation are equivalent to all the solutions of corresponding second-order differential equation by comparison theorem.And we get the oscillation condition of the second-order impulsive neutral differential equation with positive and negative coefficients.Finally,we can get two examples with this method.In Chapter 5,we summarize the full thesis.Furthermore,we also point out the next research direction.