The Stability And Boundedness Of Solutions For Several Kinds Of Nonlinear Delay Differential Equations

In this paper, the stability and boundedness of solutions for a kind of third-order and a kind of fourth-order nonlinear delay differential equations are studied by the second method of Lyapunov. Some sufficient conditions which guarantee the stability and boundedness of solutions are preasented. The main content is as follows:Firstly: we summarize the research background and the review achievements about the stability of delay differential equations in domestic.Secondly: we summarize the basic concepts, the basic theories of this article.Thirdly:we study a kind of non-linear third-order delay differential equations as follows,establish some sufficient conditions for the global asymptotic stability of the zero solution and the boundedness of all solutions to it.Fourthly: we study a kind of non-linear fourth-order delay differential equations as follows,establish some sufficient conditions for the asymptotic stability of the zero solution and the boundedness of all solutions to it.