Study On The Oscillation And Asymptotic Behavior Of Several Classes Of Third Order Neutral Differential Equations

Oscillation is a very important branch of the theory of differential equations,and it has a profound actual background. In this article, we will use a Operator method, Riccati transformation and integral averaging technique, we obtain some new results by the study of several classes of differential equations.According to the contents, we divided the article into the following chapters:Chapter 1 Preference, we introduce the main contents and its background of this paper.Chapter 2 By using a Operator method to discuss the oscillation criteria for third-order neutral delay differential equations as follow: where ?? 1 is a ratio of odd positive integers and t? t0, And we got several sufficient conditions to guarantee all solutions of the equations oscillation. And we improved the results obtained by Tian et al. In the last,one example are provided to illustrate our results.Chapter 3 We study the oscillation and asymptotic behavior of third-order neutral delay differential equations with distributed deviating arguments as follow: where ??1 is a ratio of odd positive integers and t? t0.And we got two sufficient conditions to guarantee all solutions of the equations oscillation. And we improved the results obtained by Zhang et al. In the last, one example are provided to illustrate our results.Chapter 4 By using generalized Riccati transformation to study the oscillation and asymptotic properties of third-order neutral delay differential equations with dis-tributed deviating arguments: where ??(?) is a ratio of odd positive integers and t ? t0. And we got three sufficient conditions to guarantee all solutions of the equations oscillation. And we improved the results obtained in the third part. In the last, two examples are provided to illustrate our results.Chapter 5 We study some oscillation criterions for third-order delay differential equations with distributed deviating arguments and middle term: where ??(?) is a ratio of odd positive integers and t? t0, Define a new function z by And we got two sufficient conditions to guarantee all solutions of the equations oscilla-tion. And we improved the results obtained in the third part. In the last, one example are provided to illustrate our results.