Oscillation Of Third-order Neutral Delay Differential Equations

The problem on the oscillation of third-order differential equations are important subjects in the theory of differential equations.Owing to the important in the both theory and in applications,third-order differential equations problems have been at-tracted many researchers,and some results have beenobtained.Under the impetus of differential equations and practical problems,the development of the research on the third-differential equations is rapid.However,the problems on the oscillation of third-order differential equations are the hot spot which have discussed in reccent years.In this article,we mainly investigate the oscillation behavior of the third-order neutral differential equations,the oscillation behavior of third-order neutral differential equation with continuously distributed delay.By using the generalized Riccati trans-formation and integral averaging technique,we talk about the oscillation criteria of differential equations under different conditions.The thesis is divided into four chap-tersIn chapter 1,we mainly introduce the differential equtions of the domestic and foreign research present situation,the significance of selected topic,the main work of this article.In chapter 2,we introduce the basic concept of the he oscillation behavior of the third-order neutral differential equations,and the important theorems and inequalities needed to prove the oscillationIn chapter 3,we mainly study the oscillation of third-order neutral differential equations (?) under the condition of ?t0 ? a(s)-1 ds<?,sufficient conditions for oscillation of equation are obtained.The results of exiting literatures are generalized and improved.In chapter 4,we mainly study the oscillation of third-order neutral differential equations (?) under the condition of ??1,?t0 ? a(s)-1/? ds<?,sufficient conditions for oscillation of equation are obtained.The results of existing literatures are generalized and improved.