Research Of Positive Solutions Existence To Nonlinear Boundary Value Problems For Differential Equations

Recently, many authors have given a mount of fixed point theorems. These fixed point theorems have been applied to many problems. The cone expression and compression theorem of functional type is very important among all theorems.In Chapter 1, the author brings out a brief out view of the research status of these questions.In Chapter 2 of this thesis, some basic knowledge is given on the research.In Chapter 3 of this thesis, the cone expansion and compression fixed point theorem of convex functional type and the cone expansion and compression fixed point theorem of convex functional type are combined to solve the existence of positive solutions for second-order m-point boundary value problem. Some sufficient conditions are given which guarantee the existence of positive solutions.In Chapter 4 of this thesis, the author use the same method, which is the combination of the cone expansion and compression fixed point theorem of convex functional type and the cone expansion and compression fixed point theorem of convex functional type solve the the existence of nonlinear positive solutions for second-order m-point boundary value problem. Some sufficient conditions are given which guarantee the existence of positive solutions.In Chapter 5 is the generalization of this thesis.