Qualitative Study On Two Classes Of Nonlinear Neutral Functional Differential Equations

Neutral functional differential equation has more widespread form compared with functional differential equation, which has been widely applied in physics, e-cology, genetics and such fields. Therefore, the qualitative study of neutral func-tional differential equation is significant both in theory and in practice. In addition, the researches of the problem for periodic solution and stability are two important branches of differential equation qualitative theory, which have been given attention by scholars both at home and abroad.Base on the above situation, existence of the periodic solutions for a class of neutral predator-prey model and stability of zero solution for a class of neutral Volterra integro-differential equation, which will be further discussed in this thesis. The thesis contains three chapters.Chapter 1 introduces the research significance and research dynamic about the periodicity and stability of solutions for neutral functional differential equation, then this chapter presents the main research contents and the applied research method.In Chapter 2, a class of neutral predator-prey model with Leslie-Gower Holling-type Ⅱ schemes and Michaelis-Menten-type prey harvesting is considered. By using Mawhin’s continuation theorem, we derive some sufficient conditions for the existence of positive periodic solutions of this predator-prey model. An example is presented to show the feasibility of the main result in this chapter.Using krasnoselskii fixed point theorem, Chapter 3 discusses the stability and asymptotic stability of the zero solution for the following neutral Volterra integro-differential equation The results generalize the existing results of the relevant articles.