Positive Solutions For Third Order M-point Boundary Value Problems With P-Laplacian Operator

In this paper we main study the existence of positive solutions for third order differential equation under m-point boundary value conditions with p-Laplacian op-erator, and the relation between the existence of solution and the parameter for the corresponding problem with parameter.First, we consider the existence of positive solutions of the following multi-point boundary value problem where and By using Guo-Krasnosel'skii, Leggett-Williams and some analysis technique, we establish the existence results of single, twin,three and arbitrary number of positive solutions. Then, under the hypothesis of p= 2 and f has monotonicity condition, we discuss the uniqueness of the positive solution of the above problem, and give some examples to illustrate the main results.Then we discuss p-Laplacian third order m-point boundary value problem with parameter the relation between the existence of single or twin solution, nonexistence of solution and the parameter is established. The main tool are Guo-Krasnosel'skii fixed point theorem and Leray-Schauder fixed point theorem.