Existence Of Solutions For Boundary Value Problems Of Some Ordinary Differential Equations

The boundary value problem of ordinary differential equation is abstracted from the problems of natural science and project technology, it is extensively applicated in subject of hydromechanics, mechanics of materials, astronomy, economics, biology, medicine etc. For the type of ordinary differential equations which can be solved is very few, it is difficult to get the solutions of the boundary value problem. In order to adapt the actual problem demand, we have to research the property of the solution. Thus, we should firstly solve that whether the solution of the boundary value problem exist? Whether only? This is the basic problem of boundary value problem. In this paper, the main work is to research the existence of solutions for boundary value problems of some ordinary differential equations, and gives the judge gist of the existence of solutions. The following is the main contains.In chapter one, it is a brief introduction of the history and present situation of the study about the boundary value problems of the ordinary different equation. With two actual examples, we show that the research of the existence of solutions for boundary value problems of ordinary differential equations not only has important theory significance, but also has vital practical significance.In chapter two, by the uses of a Leggett-Williams fixed-point theorem, we get the existence of multiple positive solutions for systems of second-order two-point ordinary differential equations, which the non-linear item includes the first order derivative. For merly, the research to the ordinary differential equation systems, its non-linear item did n't reveal includes the first order derivative. In this chapter, we research the problem, which the non-linear item includes the first order derivative. And get the existence of multiple positive solutions.In chapter three, by the uses of the Leray-Schauder theory, we get the existence of positive solutions for fourth-order three-point boundary value problem under the barrier strips conditions. In this chapter, we apply the barrier strip skill in the high order and multi-point boundary value problem, and get the existence of positive solutions for a fourth-order three-point boundary value problemIn chapter four, by the uses of the monotone iterative technique, we get the existence and iteration of positive solutions for a generalized p-laplace boundary value problem with Sturm-Liouville boundary conditions. The research to the p-laplace boundary value problem has got a lot of results. In this chapter, the research object is a generalized p-laplace boundary value problem, and the result is a extend of the formerly the theory.