一类分数阶微分方程多点边值问题正解的存在性  

Positive Solutions of Multi-point Boundary Value Problem for a Class of Fractional Differential Equations

作　　者：赵微 ZHAO Wei(Department of Teaching Education,Daqing Normal University,Daqing 163712,Heilongjiang)

机构地区：[1]大庆师范学院教师教育学院,黑龙江大庆163712

出　　处：《四川师范大学学报（自然科学版）》2020年第3期326-332,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：黑龙江省青年科学基金项目(QC2009C99);吉林省教育厅“十三五”科学技术项目(JJKH20200235KJ);大庆市科技计划项目(ZD-2017-49)。

摘　　要：讨论一类分数阶微分方程多点边值问题.首先研究其格林函数及相关性质,构造一个特殊的锥.其次通过与一个线性算子相关的第一特征值的讨论,运用不动点指数定理,得到了该边值问题正解存在的结果.最后给出一个例子用以说明定理的应用.In this paper,we discuss one class of fractional differential equations with multi-point boundary value problem. First,we study the Green function and obtain its properties. Second,construct a special cone and get the existence of positive solutions under some conditions concerning the first eigenvalue of the relevant linear operator by using fixed point index theory. Finally,an example is given for the application of the theorem.

关 键 词：分数阶微分方程 多点边值问题 格林函数 正解 不动点指数 

分 类 号：O175.8[理学—数学]