一类Caputo分数阶微分方程多点边值问题的多解性  

A Class of Caputo Fractional Differential Equation with Multiple Solutions for Multi-point Boundary Value Problem

作　　者：黄燕萍 韦煜明 HUANG Yanping;WEI Yuming(College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China)

机构地区：[1]广西师范大学数学与统计学院,桂林541004

出　　处：《应用泛函分析学报》2018年第2期157-165,共9页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11361010);广西自然科学基金(2014GXNSFAA118002);广西高等学校高水平创新团队及卓越学者计划资助;广西高校数学与统计模型重点实验室开放基金课题研究计划资助

摘　　要：本文讨论了一类Caputo分数阶微分方程多点边值问题的多解性,通过把分数阶微分方程的边值问题转化成与其等价的积分方程问题求出边值问题的Green函数并得到其格林函数的相关性质,最后利用锥上不动点指数定理研究分数阶微分方程多点边值问题正解和多个正解的存在性.In this paper, we discuss the multiple solutions for a class of Caputo fractional differential equation for multi-point boundary value problem. The fractional differential equation boundary value problem is converted into equivalent integral equation to calculate the boundary value problems of the Green function and analyses the nature of the Green function. Last, the existence of solutions and multiple positive solutions of boundary value problem is obtained by using the fixed point index theory.

关 键 词：分数阶微分方程 多点边值问题 不动点指数理论 多解性 

分 类 号：O175.1[理学—数学]