《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (10): 95-103.

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1. 山东师范大学数学与统计学院, 山东 济南 250014
• 出版日期:2020-10-20 发布日期:2020-10-07
• 作者简介:孙妍妍(1995— ),女,硕士研究生,研究方向为非线性微分方程. E-mail:yysun0321@163.com
• 基金资助:
国家自然科学基金资助项目(11671237)

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

SUN Yan-yan, LIU Yan-sheng

1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, Shandong, China
• Online:2020-10-20 Published:2020-10-07

Abstract: 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.

• O175.8
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