Global Structures And Existence Of Solutions For Three-point Boundary Value Problems

Since the ordinary differential boundary value problem has been put forward,it becomes more widely used,and it also has great significance in solving mechanics,air science and cybernetics.And it has become an important object of study for many mathematics and other scholars.In this paper,we discuss the existence of solutions for three-point boundary value problems and its global structures by using Rabinowitz global theorem.This thesis is divided into two chapters.In the first chapter,we discuss the three-point boundary value problem where ?? 0,,:[0,1]× R ? R is continuous,and f(t,0)? 0,with ?>1,0 ?? ?1.In this chapter,we use the global theorem to discuss the existence of node solutions.Firstly,the properties of its operator eigenvalue are obtained.And then,the global structure theory is further discussed.Finally,we get the results of the existence of the nodal solutions.In the second chapter,we consider the existence of multiple nodal solutions to the following boundary value problem where ?>0,?>1,? E(0,1),f is a continuous function but does not require non-negative.First,this section established the Shrinking core W.And then,we obtain the eigenvalues of linear operators and the properties of eigenvalues.Based on the Rabinowitz global theorem,we get the conclusion of the existence of nodal solutions by the topological degree method.In the last part,letting ? = 1,we obtain the extended fixed point theorem and the multi-solution theorem in the set of W,and we also receive the existence of multiple solutions by these theorems.