一类分数阶四点边值问题正解的存在性

doi:10.13438/j.cnki.jdzk.2022.02.001

吉首大学学报（自然科学版） ›› 2022, Vol. 43 ›› Issue (2): 1-6.DOI: 10.13438/j.cnki.jdzk.2022.02.001

• 数学 • 下一篇

一类分数阶四点边值问题正解的存在性

潘欣媛,何小飞

(1.吉首大学数学与统计学院，湖南吉首 416000；2.吉首大学张家界学院，湖南张家界 427000)

出版日期:2022-03-25 发布日期:2022-07-14
通讯作者: 何小飞(1971—),男,湖南新邵人,吉首大学张家界学院教授,博士,主要从事微分方程与动力系统研究.
作者简介:潘欣媛(1998—),女,湖南城步人,吉首大学数学与统计学院硕士研究生,主要从事微分方程与动力系统研究
基金资助:
吉首大学研究生校级科研项目（JDY21019）

Existence of Positive Solution for a Class of Fractional Four-Point Boundary Value Problems

PAN Xinyuan,HE Xiaofei

(1.College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China;2.Zhangjiajie College,Jishou University,Zhangjiajie 427000,Hunan China)

Online:2022-03-25 Published:2022-07-14

摘要/Abstract

摘要：利用Green函数、Arzela-Ascoli定理及锥上不动点定理,研究了一类含p-Laplacian算子的分数阶微分方程边值问题正解的存在性.

关键词： 分数阶微分方程, p-Laplacian算子, Green函数, 不动点定理, 正解

Abstract: By applying Green's function,Arzela-Ascoli theorem and fixed point theorem on cones,the existence of positive solution is obtained for a class of p-Laplacian type fractional differential boundary value problems.

Key words: fractional differential equation, p-Laplacian operator, Green's function, fixed point theorem, positive solution

潘欣媛, 何小飞. 一类分数阶四点边值问题正解的存在性[J]. 吉首大学学报（自然科学版）, 2022, 43(2): 1-6.

PAN Xinyuan, HE Xiaofei. Existence of Positive Solution for a Class of Fractional Four-Point Boundary Value Problems[J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(2): 1-6.

参考文献

[1] KILBAS ANATOLY A,SRIVASTAVA HARI M,TRUJILLO JUAN J.Theory and Applications of Fractionaldifferential Equations[M].Amsterdam:Elsevier,2006:67-75;90-91.
[2] 郭大钧,孙经先,刘兆理.非线性常微分方程泛函方法[M].济南:山东科学技术出版社,1995:118.
[3] LI Shuai,ZHANG Zhixin,JIANG Wei.Multiple Positive Solutions for Four-Point Boundary Value Problem of Fractional Delay Differential Equations with p-Laplacian Operator[J].Applied Numerical Mathematics,2021,165(53):348-356.
[4] LI Yunhong,JIANG Weihua.Existence and Nonexistence of Positive Solutions for Fractional Three-Point Boundary Value Problems with a Parameter[J].Journal of Function Spaces,2019,2019:1-10.
[5] ZHAO Yige.On the Existence for a Class of Periodic Boundary Value Problems of Nonlinear Fractional Hybrid Differential Equations[J].Applied Mathematics Letters,2021,121:107368-107373.
[6] LIU Xiping,JIA Mei,GE Weigao.The Method of Lower and Upper Solutions for Mixed Fractional Four-Point Boundary Value Problem with p-Laplacian Operator[J].Applied Mathematics Letters,2017,65:56-62.
[7] TIAN Yuansheng,BAI Zhanbing,SUN Sujing.Positive Solutions for a Boundary Valueproblem of Fractional Differential Equation with p-Laplacian Operator[J].Advances in Difference Equations,2019,2019(1):349-362.
[8] LI Xiaoping,HE Minyuan.Monotone Iterative Method for Fractional p-Laplacian Differential Equations with Four-Point Boundary Conditions[J].Advances in Difference Equations,2020,2020(1):686-698.
[9] ZHOU Jianwen,DENG Yumei,WANG Yanning.Variational Approach To p-Laplacian Fractional Differential Equations with Instantaneous and Non-Instantaneous Impulses-Science Direct[J].Applied Mathematics Letters,2020,104:106251-106259.
[10] LI Dongping,CHEN Fangqi,WU Yonghong,et al.Multiple Solutions for a Class of p-Laplacian Type Fractional Boundary Value Problems with Instantaneous and Non-Instantaneous Impulses[J].Applied Mathematics Letters,2020,106:106352-106329.

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一类分数阶四点边值问题正解的存在性

Existence of Positive Solution for a Class of Fractional Four-Point Boundary Value Problems

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