| 一类非线性Riemann-Liouville适型分数阶微分方程正解的存在性 |
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| 引用本文： | 彭钟琪,李媛,毕国健,薛益民.一类非线性Riemann-Liouville适型分数阶微分方程正解的存在性[J].吉林大学学报(理学版),2023,61(1):23-31. |
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| 作者姓名： | 彭钟琪 李媛 毕国健 薛益民 |
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| 作者单位： | 1. 沈阳工业大学 理学院, 沈阳 110870； 2. 徐州工程学院 数学与统计学院, 江苏 徐州 221018 |
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| 基金项目： | 国家自然科学基金数学天元基金(批准号：11526177)；;江苏省自然科学基金(批准号：BK20151160)； |
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| 摘 要： | 首先，利用Green函数的性质和Guo-Krasnosel’skii’s不动点定理，证明一类非线性Riemann-Liouville适型分数阶微分方程正解的存在性，给出该问题至少存在两个正解的结果；其次，基于一个比较原则，利用单调迭代技巧和上下解方法证明该问题极值解的存在性.
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| 关 键 词： | 分数阶微分方程 单调迭代技巧 极值解 不动点定理 |
| 收稿时间： | 2021-12-17 |
Existence of Positive Solutions for a Class of Nonlinear Riemann-Liouville Conformable Fractional Differential Equations |
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| PENG Zhongqi,LI Yuan,BI Guojian,XUE Yimin.Existence of Positive Solutions for a Class of Nonlinear Riemann-Liouville Conformable Fractional Differential Equations[J].Journal of Jilin University: Sci Ed,2023,61(1):23-31. |
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| Authors: | PENG Zhongqi LI Yuan BI Guojian XUE Yimin |
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| Institution: | 1. School of Science, Shenyang University of Technology, Shenyang 110870, China；
2. School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, Jiangsu Province, China
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| Abstract: | Firstly, we proved the existence of positive solutions for a class of nonlinear Riemann-Liouville conformable fractional differential equations by using the properties of Green’s function and Guo-Krasnosel’skii’s fixed point theorem, and obtained that there were at least two positive solutions to the problem. Secondly, based on a comparison principle, we proved the existence of extremal solutions to the problem by using the monotone iterative technique and the method of upper and lower solutions. |
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| Keywords: | fractional differential equation monotone iterative technique extremal solution fixed point theorem |
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