On The Study Of Positive Solutions To Boundary Value Problem For Nonlinear Differential Equations

Boundary value problems for nonlinear differential equations play a very important role in both theory and applications. They are used to describe a large number of physical biological and chemical phenomena. In recent years, there has been a great deal of research works on boundary value problems for second or higher order differential equations. And boundary conditions are most simple type. Studying higher order and complex boundary value problems is still small. So this paper studies the problem is:by the cone expansion and compression fixed point theorem, which studies the existence of positive solutions of fourth-order multi-point boundary value problem.In chapter1, the development of the boundary value problem and background of the relevant question are summarized briefly.In chapter2, by the cone expansion and compression fixed point theorem, we consider the existence of positive solutions of fourth-order multi-point boundary value problem.In chapter3, we will continue to discuss the existence of positive solutions of fourth-order multi-point boundary value problem.In this chapter, In this chapter, we will change the scope of m-2∑i=1αi, Similarly, we make use of the cone expansion and compression fixed point theorem to get our conclusion.