Qualitative Study On Two Classes Of Neutral Functional Differential Equations

Neutral functional differential equation has gathered a lot of public interest by scholars both at home and abroad beause of its important research value in the physical, biological, contral and such fields. The existence of periodic solution for the equation has achieved good results. But, the research results about the neutral functional differential equation with impulse were not so much because of its complex form. Many literatures have only obtained that the zero solutions of the neutral functional differential equation is stable in C.For the reasons given above, the periodic solutions for a class of neutral predator-prey model with impulse and the stability in C1 of the zero solution for a class of neutral functional differential equation will be further discussed in this thesis. Three chapters are contained.In Chapter 1, the research background and present situation of the existence of the periodic solutions and stability of the zero solution for the neutral functional differential equation are discussed. Then this chapter also presents the specific contents and research methods.In Chapter 2, by means of Mawhin continuation theorem of coincidence degree theory, the existence of the positive periodic solution for the following nonlinear neutral predator-prey model with impulse and Holling-type III functional response is studied. Our results generalize the corresponding results in some existing litera-ture.In Chapter 3, we study the following linear neutral functional differential equa-tion By using fixed-point, we obtain the global asymptotic stability in C1 of the zero solution. The corresponding results of the literature are extended and improved.