Positive Solutions Of Three Kinds Of Third-order Boundary Value Problems For Ordinary Differential Equations

This thesis mainly focuses on the existence of the positive solutions to three kinds of multi-point boundary value problems for ordinary differential equations. The argument is based on the Krasnosel'skii fixed point theorem together with the method of upper and lower solutions and the monotone iterative. The main results are as follows:1. A class of third-order three-point singular boundary value problem are concerned. Here ?? (0,1), ?,?> 0, ? is a positive parameter. The nonlinearity f(t,u) in the ordinary differential equation may not be nonnegative and may be allowed to have singularities at t= 0 or t= 1. The existence results of positive solution are obtained by using the Krasnosel'skii fixed point theorem.2. The following third-order four-point singular boundary value problems are concerned, where ?,? (0,1), ?,?? (0,1),?(1-?)< 1, ? is a positive parameter. This thesis have computed the Green function and further analyzed some properties. In addition, an appropriate positive cone in Banach space C[0,1] is constructed. The existence results of positive solution are obtained by using the Krasnosel'skii fixed point theorem.3. A class of third-order four-point boundary value problem with derivative term is concerned, where ?,? (0,1), ?,?? (0,1),?(1-?)< 1. The existence results are obtained by using the method of upper and lower solutions and the monotone iterative.