The Problem Of Periodic Solutions For P-Laplacian Neutral Functional Differential Equation And Ratio-dependent Predator-prey System

Behavior of the solutions is a basic problem of diferential equationstheory, its an important aspect is ascertaining the existence of periodicsolutions for equations or system and under what conditions exist peri-odic solution. This has been considered by many scholars.In this paper, a ratio-dependent predator-prey system and ap-Laplacian neutral Rayleigh equation are researched. we obtian the exis-tence of periodic solutions of them by using the theory of coincidence de-gree and extension of Mawhin’s continuation theorem respectively. Thisdissertation is divied into four chapters.In the first chapter, we introduce the background of ratio-dependentpredator-prey system and the development situation of neutral functionaldiferential equation, covering the content, related concepts and lemmas.In the second chapter, by using extension of Mawhin’s continuationtheorem, we study the existence of periodic solutions to ap-Laplacianneutral Rayleigh equation with deviating arguments.In the third chapter, we investigate a ratio-dependent three-speciespredator-prey system with the Beddington-DeAngelis functional response,and use coincidence degree theory to prove that it exists periodic solu-tions.In the fourth chapter, the research content is summarized and futureprospect is put forward.