Positive Solutions Of Fourth-Order Four-Point Sturm-Liouville Boundary Value Problems

Recently, with the development of science and technology, a lot of mathematical models which are described by boundary value problems (BVPs for short) of differ-ential equations. The BVPs of fourth-order differential equations arise in different fields of applied mathematics and physics, which especially have wide applications in elasticity and stability theory. Therefore, it is significant to study the BVPs of fourth-order differential equations.In this thesis, we firstly investigate some fourth-order four-point Sturm-Liouville BVP. The existence of positive solution to the fourth-order four-point Sturm-Liouville BVP is obtained under stronger or weaker conditions, respectively, by using the fixed point theorem concerning cone expansion and compression of norm type. Next, we are concerned with some fourth-order four-point Sturm-Liouville BVPs with two or four parameters. We not only prove the existence and uniqueness of a positive solu-tion for the BVPs, but also study the dependence of this solution on the parameters.