The Existence Of Positive Solutions For Second-order Nonlinear Differential Equations With Boundary Value Problems

Nonlinear Functional Analysis as an important branch of modern mathematics, because avariety of natural phenomena well explain the nature by the widespread concern of thegrowing number of mathematicians. Among them, the nonlinear edgevalue due to the widerange of applications in the field of physics, applied mathematics, aerospace, biological, isone of the most active areas of research analysis in mathematics.Based on extensive practical application background, the existence of non-linearordinary differential equation boundary value problem in the entire Ordinary DifferentialEquations research area is particularly important, especially second-order ordinary differentialequation boundary value problem has been in the field of differential equations studyanimportant research topic.This paper study nonlinear second order boundary value problem, to discuss the twotypes of nonlinear second order boundary value problem, Existence of Positive Solutions for aclass of nonlinear second order two point boundary value and a class of non-linearsecond-order three-point boundary value problem under appropriate assumptions, respectively,illustrates the two types of boundary value problems. Existence of Solutions and Existence ofPositive Solutions has given proof. Gives some new results for nonlinear second orderboundary value problems existence of positive solution theory.Paper is divided into three chapters:In the first chapter on the historical background and development of the nonlineardifferential equation boundary value problem, and summarizes the current domestic andinternational research profiles of the nonlinear differential equation boundary value problem,the level and development trend.In the second chapter, we studied a class of nonlinear second-order two-point boundaryvalue problemConstruct Green's function and is given the upper and lower bounds, by defining thecompletely continuous operator to derive the equivalent integral equation, and using the conefixed point theorem Existence of Positive Solutions to certify.In the third chapter,we studied a class of nonlinear second-order three-point boundaryvalue problem Similar to the second chapter,construct Green's function and gives the upper and lowerbounds estimated by defining the completely continuous operator obtained the equivalentintegral equation, and then use the cone fixed point theorem to prove the existence of positivesolutions.