一类非线性Riemann-Liouville适型分数阶微分方程正解的存在性  

Existence of Positive Solutions for a Class of Nonlinear Riemann-Liouville Conformable Fractional Differential Equations

作　　者：彭钟琪 李媛[1] 毕国健 薛益民[2] PENG Zhongqi;LI Yuan;BI Guojian;XUE Yimin(School of Science,Shenyang University of Technology,Shenyang 110870,China;School of Mathematics and Statistics,Xuzhou University of Technology,Xuzhou 221018,Jiangsu Province,China)

机构地区：[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

出　　处：《吉林大学学报（理学版）》2023年第1期23-31,共9页Journal of Jilin University:Science Edition

基　　金：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);徐州工程学院科技培育项目(批准号:XKY2017113)。

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.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.

关 键 词：分数阶微分方程 单调迭代技巧 极值解 不动点定理 

分 类 号：O175.8[理学—数学]