Existence And Multiplicity Of Solutions For Fourth-order Three-point Boundary Value Problems

The formation and development of ordinary differential equations are closely related to the development of mechanics,physics and other subjects. In recent years, with the continuously progress of science and technology, many achievements need the related theory of nonlinear analysis and differential equations with boundary value problem as the theoretical support. And the researchers pay more and more attention to the nonlinear problems. Therefore, the study of boundary value problems of nonlinear differential equation has very important significance and practical value. The existence and multiplicity of solutions is investigated in the paper for the two kinds of fourth-order three-point boundary value problems.In the paper, there are four chapters,and the content is as follows:In chapter 1, the first part mainly introduces the symbols, definitions and theorems referenced in the paper; The second part summarizes the development, research significance and status of the nonlinear fourth-order boundary value problems; The last part introduces the arrangements of the main contents of the paper.In chapter 2, the existence and multiplicity of positive solutions is investigated by using the Avery-Peterson fixed-point theory for the following fourth-order three-point boundary value problem or We obtain some sufficient conditions of the existence of triple positive solutions of the boundary value problem.In chapter 3, the existence of solutions and positive solutions for the fourth-order three-point integral boundary value problem is studied.We use the Leray-Schauder fixed-point theorem, and obtain a sufficient condition of the existence of solutions for the three-point integral boundary value problem under the derivative of unknown function in the nonlinear term. By constructing a function we also obtain a sufficient condition for the existence of positive solutions of the problem.In chapter 4, the full paper is summarized, and we will put forward the direction of the following research.