Periodic Solutions And Boundary Value Problems Of Several Kinds Of Differential Equations

In this paper,we mainly consider the periodic and asymptotically periodic solutions on coupled integro-differential systems with impulses,the existence and global exponential stability of periodic solutions for Nicholson fly model with continuous distributed delays and the existence of three positive solutions for the third-order three-point boundary value problems.This thesis is composed of four chapters.In Chapter 1,we describe briefly the research background and the main work of this paper.In Chapter 2,we discuss the existence of periodic solutions and asymptotic periodic solutions for impulsive coupled integral-differential systems.In this paper,we consider impulsive differential equations which are more realistic.The main method is to transform differential equations into integral equations.We obtain sufficient conditions for the existence of periodic solutions and asymptotic periodic solutions by using Schauder fixed point theorem.In Chapter 3,we discuss the existence and global exponential stability of periodic solutions for Nicholson fly model with continuous distributed delays.We prove the global exponential stability of periodic solutions by constructing Lyapunov functions.In Chapter 4,we consider the existence of multiple positive solutions for third-order three-point boundary value problems.By using the five functional fixed point theorem,we prove that there are at least three positive solutions by analyzing the properties of kernel function.