Positive Solutions For Singular Nonlinear Higher Order Ordinary Differential Equation With Boundary Value Problems

In this paper,We are concerned with positive solutions of singular higher order ordinary differential equation's boundary value problem,It permits a(t) to have singularity at endpoint t = 0, t = l,and permits a(t) to be noncontinuous at (0,1).In this paper, we permit rn ^ 0,and obtain at least one solution of (l)in Theorem 1 and at least two solutions of (l)in Theorem 2 under the different conditions.It is different in the method of proving between [Ijand Theorem 1. The authors of [Ijdon't obtain the expressions of the Green's functions. They prove the results of (1) by turning the Green's functions from high dimension to low dimension, then useing the properties of the Green's functions with low dimension. But in this paper,we calculate firstly the expressions of the Green's functions ,then estimate its properties using the expressions, we use the similar method with [2][3] in Theorem 2.