具p-Laplacian算子三阶脉冲方程三点边值问题的正解

Positive solutions of three-point boundary value problems for third-order impulsive differential equations with a p-Laplacian operator

考察了一类具p-Laplacian算子三阶脉冲方程三点边值问题的正解。利用二阶脉冲方程三点边值问题的Green函数,把该类问题转化为一个等价的积分方程,在适当的锥上应用Avery-Peteron不动点定理讨论该类积分方程的正解存在性,得到了三个正解存在的充分条件。

The positive solution of three-point boundary value problem for third-order impulsive differential equations with a p-Laplacian operator is considered.This problem is transformed into an equivalent integral equation by applying the Green＇s function of three-point boundary value problem for second-order impulsive differential equations.The existence of the positive solution is discussed by applying Avery-Peteron fixed point theorem on a suitable cone.Thus a sufficient condition is obtained for the existence of three positive solutions.