Existence Of Solutions For Second-Order Boundary Value Problems Of Some Ordinary Differential Equations

Ordinary differential equation is an important branch of modern analytic mathematics. It is extensively used in natural science and project technology, for example, the subject of hydromechanics, mechanics of materials, astronomy, economics, biology, medicine can be abstracted to solve the boundary value problems. The study of semilinear elliptic equation boundary value problem at resonance was initiated by Landesman and Lazer in 1970. Since then, the study of boundary value problems of nonlinear differential equations at resonance has got a lot of important results within 30 years. Especially the study of the classical boundary value problems of nonlinear differential equation at resonance (for example:Dirichlet boundary value problem, Neumann boundary value problem, periodic boundary value problem) have got a lot of systematic and profound results. But so far, very few results were established for nonlinear multi-point boundary value problems at resonance. In this paper, the main work is to research the existence of the solution for some second-order multi-point boundary value problems at resonance. The paper contains three chapters.In chapter one, a brief introduction of the history and present situation of the study about the boundary value problems of the ordinary different equation is given. And a introduction of the results of the study about the nonlinear ordinary different equation at resonance is given.In chapter two, by means of calculation of the method of lower and upper solutions we get the existence of the solutions for some nonlinear three-point differential systems at resonance.In chapter three, by the use of the Mawhin theorem, we study the existence and the uniqueness of the solutions for some nonlinear three-point differential systems at resonance.