Two Classes Of Boundary Value Problems With A Predator - Prey System

Recent years, differential equations with boundary value conditions have been extensively studied by many authors. In this paper, we mainly investigate two classes of differential equations and a class of predator-prey system with boundary value conditions. We divide this article for four chapters. In chapter 1, we introduce the historical background of the problems and main works of this paper, definitions and properties we need in this paper are also given. Chapter 2 is devoted to studying the existence of solutions for second order nonlinear impulsive differential equations with periodic boundary value conditions by means of Schaefer's fixed-point theorem. In chapter 3, applying fixed-point theorem in cones, we study positive solutions for nonlinear triple-point problem on time scales. We mainly discuss the existence of periodic solutions of a delayed predator-prey system on time scales based on coincidence degree theorem in chapter 4.