The Constructive Proof And Calculation Of The Solutions Of Boundary Value Problem Of Ordinary Differential Equation

The main topic of this paper is the periodic solutions of ordinary differential equations.Periodic movements are common phenomenon of nature and the fields of human activity, the periodicity problem plays a central role in the qualitative theory of ordinary differential equations. As an important aspect of application, finding periodic solutions of ordinary differential equations is an attracting topic. In this paper, with initial value problems method, a constructive proof of periodic solutions of several special kinds of ordinary differential equations is given. Meanwhile, with the use of the homotophy continuation method, some examples are computed. This approach provides a global method for finding periodic solutions of these several kinds of equations.The constructive proof of Newton Equation and Duffing Equation with polar coordinates is given by Li Weiguo. The advantage of this method is that it has a wider application range, but the process of its proof need skills and difficult to structure. We give a constructive proof of several special kinds of ordinary differential equations for its particular. This method is intuitive, simple and easy to understand, but its application range is narrow.This paper consists of four chapters. In Chapter 1, we introduce the present situation of the periodic solutions of ordinary differential equation and finding periodic solutions with homotophy continuation method. In Chapter 2, we discuss the constructive proof given by Li, In Chapter 3, we give a constructive proof for several particular kinds of ordinary differential equations with different method. In Chapter 4, we use the same method give the constructive proof of semi-periodic solutions of the equations we discuss in Chapter 3.