The Existence Of Positive Solutions For Boundary Value Problems Of Differential Equations

In this paper, we mainly talk about the existence of positive solutions for three types of differential equation boundary value problems.Firstly,we investigate the existence of positive solutions for third-order two-point boundary value problems with integral boundary condition. By using Krasnosel-skii fixed point theorem, the existence of positive solution is obtained. The properties of the corres-ponding Green function is the key of this result. One example is given to show the main results.Secondly, we consider a second-order three-point boundary value problems with p-Laplace operator, by using the Krasnosel-skii fixed point theorem, we obtain one positive solution of Boundary Value Problems. The properties of the corresponding operator is the key to this conclusion.Finally, we study the existence of positive solutions for fractional differential equations boundary value problems with integral boundary conditions, by using the Krasnosel-skii fixed point theorem and Leggett-Williams fixed point theorem respectively, some existence and multiple positive solutions are obtained. Two examples are given to illustrate our results.