Stability And Approximate Representation Of Nonoscillatory Solutions Of Neutral Functional Differential Equations

Neutral functional differential equation is an important class of functional dif-ferential equation. At the same time, its application is quite extensive, involving physical, biological, engineering and other areas. Due to the complexity of the structure of the equation, the research is different from the non-neutral case about the existence nonoscillatory solution and qualitative research of neutral functional differential equation. Therefore the related research has important theoretical sig-nificance and obvious practical value. Currently, the research is not much for the stability of neutral functional differential equation. However, many results about the existence of the functional differential equation have been only given sufficient conditions for the existence of the solution, but no one has given approximate rep-resentation for the solution. In fact, that will be more valuable in the application if we give an approximate representation for the existence of the solution of the functional differential equation.Based on the above reasons, this paper discusses the stability and approximate representation of nonoscillatory solutions of neutral functional differential equation.In Chapter 1, the domestic and foreign research of functional differential equa-tion is summarized. In addition, this chapter shows the background about the stability and approximate representation of nonoscillatory solutions of differential equation. Finally, this chapter also presents the research contents and methods in this paper.Using Banach fixed point principle, Chapter 2 shows the sufficient condition to ensure that the zero solution of neutral differential equation with impulses is asymptotically stable. And the results extend and improve the results of the existing literature.Using Banach fixed point principle, Chapter 3 shows the sufficient conditions to ensure that the nonoscillatory solutions is existing about the nth-order nonlinear neutral functional differential equation In addition, this paper constructs a iterative approximation schemes for these nonoscil-latory solutions and establishes error estimates.