Existence Of Monotone Positive Solutions For Two Classes Of Elastic Beam Equation Boundary Value Problem

Recently, with the development of science and technology, a lot of mathematicalmodels are described by boundary value problems (BVPs) of di?erential equations.The BVPs of fourth-order di?erential equations arise in di?erent fields of appliedmathematics and physics, which especially have wide applications in elasticity andstability theory. Therefore, it is significant to study the BVPs of fourth-order dif-ferential equations.The paper is divided into three chapters:Chapter 1 is the introduction of this paper, which introduces the studying back-ground of this thesis and our main works. In addition, we list some preliminaryknowledge needed in this paper.In chapter 2, we consider the existence and iteration of monotone positivesolutions of BVP for an elastic beam equation. An example is also included toillustrate the main results.In chapter 3, we discuss BVP for an elastic beam equation with nonlinearboundary conditions. By applying monotone iteration method, we not only obtainthe existence of monotone positive solutions, but also two iterative sequences ofmonotone positive solutions are given. It is worth mentioning that these iterativeschemes start o? with zero or quadratic function, which is very useful and feasiblefor computational purpose.