Sharp Conditions For The Existence Of Positive Solutions Of Three Kinds Of Singular Differential Equations

In this paper,we mainly discuss the sharp conditions for the existence of positive solutions to three types of singular differential equations.The full text is divided into five chapters as follows:In Chapter 1,we introduce the background,significance and the current research status of the two-point boundary value problems,multi-point boundary value problems and impulsive problems.We also briefly introduce the research content of this paper and finally give the basic concepts and theorem.In Chapter 2,we study the existence and sharp conditions of the positive solutions of the second-order singular nonlocal problems.By constructing the cone and using the fixed point theorem of cone extension and compression,the sharp condition for the existence of a positive solution to the problem is obtained.In Chapter 3,we investigate the sharp conditions for the existence of positive solutions of second-order multipoint singular impulsive differential equations.We convert the equation to the form without impulse,and the fixed point theorem of cone extension and compression is used to obtain the sharp condition for the existence of a positive solution to the equation.In Chapter 4,we study the sharp conditions for the existence of positive solutions of fourth-order singular multipoint impulsive differential equations.The fourth-order equation is converted into two second-order equations,and the fixed point theorem of cone extension and compression is used to obtain the sharp conditions for the existence of a positive solution to the equation.In Chapter 5,we summarize and prospect the conclusions of this article.