抽象空间中Hadamard分数阶微分方程奇异边值问题正解的存在性  

Existence of positive solutions for singular boundary value problems of Hadamard fractional differential equations in abstract space

作　　者：孙妍妍 刘衍胜[1] SUN Yan-yan;LIU Yan-sheng(School of Mathematics and Statistics,Shandong Normal University,Jinan 250014,Shandong,China)

机构地区：[1]山东师范大学数学与统计学院,山东济南250014

出　　处：《山东大学学报（理学版）》2020年第10期95-103,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11671237)。

摘　　要：研究了Banach空间中奇异边值问题正解的存在性。通过构造一个特殊的锥,利用严格集压缩算子的不动点指数理论,建立了该边值问题的近似问题至少有两个正解的存在性。然后借助Ascoli-Arzela定理,利用近似问题解序列的相对紧性,得到边值问题至少有两个正解的充分条件。The existence of positive solutions of singular boundary value problems in Banach space is investigated.By constructing a new cone and using the fixed point index theory of strict set compression operator,it is established that there are at least two positive solutions for the corresponding approximation of the boundary value problem.Then,using Ascoli-Arzela theorem and the relative compactness of the sequence of solutions,a sufficient condition is obtained for the existence of multiple positive solutions to boundary value problem.

关 键 词：Hadamard分数阶导数 锥 奇异边值问题 

分 类 号：O175.8[理学—数学]