一类具有p-Laplacian算子的分数阶差分方程边值问题的正解

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 402-414.

一类具有p-Laplacian算子的分数阶差分方程边值问题的正解

徐家发^1,*(),罗洪林¹(),刘立山²()

¹ 重庆师范大学数学科学学院重庆 401331
² 曲阜师范大学数学科学学院山东曲阜 273165

收稿日期:2020-03-08 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 徐家发 E-mail:xujiafa292@sina.com;luohonglin@cqnu.edu.cn;mathlls@163.com
作者简介:罗洪林, E-mail: luohonglin@cqnu.edu.cn|刘立山, E-mail: mathlls@163.com
基金资助:
国家自然科学基金(11871302);国家自然科学基金(11601048);中国博士后项目(2019M652348);重庆市自然科学基金(cstc2020jcyj-msxmX0123);重庆市教委科技项目(KJQN202000528);重庆市教委科技项目(KJQN201900539);重庆师范大学青年拔尖人才资助项目(02030307/0040);重庆师范大学数学科学学院重点实验室开放课题(CSSXKFKTM202003)

Positive Solutions for a Class of Fractional Difference Equations Boundary Value Problems with p-Laplacian Operator

Jiafa Xu^1,*(),Honglin Luo¹(),Lishan Liu²()

¹ School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
² School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165

Received:2020-03-08 Online:2021-04-26 Published:2021-04-29
Contact: Jiafa Xu E-mail:xujiafa292@sina.com;luohonglin@cqnu.edu.cn;mathlls@163.com
Supported by:
the NSFC(11871302);the NSFC(11601048);the Postdoctoral Program of China (2019M652348), the NSF of Chongqing(2019M652348);the NSF of Chongqing(cstc2020jcyj-msxmX0123);the Projects of Chongqing Commission of Science and Technology(KJQN202000528);the Projects of Chongqing Commission of Science and Technology(KJQN201900539);Young Talent of Chongqing Normal University(02030307/0040);the Key Laboratory Open Issue of School of Mathematical Science, Chongqing Normal University(CSSXKFKTM202003)

摘要/Abstract

摘要：

该文研究一类具有p-Laplacian算子的分数阶差分方程边值问题.借助离散型Jensen不等式，考虑该问题与相应的不带有p-Laplacian算子的分数阶差分方程边值问题之间的关系，并运用不动点指数理论获得该问题正解的存在性.

关键词: 分数阶差分方程, 边值问题, 正解, 不动点指数

Abstract:

In this paper, we study a class of fractional difference equations boundary value problems with p-Laplacian operator. By virtue of the discrete Jensen inequalities, some relations between the considered problem and the corresponding problem without the p-Laplacian are established, and using the theory of fixed point index, the existence of positive solutions for the considered problem is obtained.

Key words: Fractional difference equations, Boundary value problem, Positive solution, Fixed point index

中图分类号:

O175.15

徐家发,罗洪林,刘立山. 一类具有p-Laplacian算子的分数阶差分方程边值问题的正解[J]. 数学物理学报, 2021, 41(2): 402-414.

Jiafa Xu,Honglin Luo,Lishan Liu. Positive Solutions for a Class of Fractional Difference Equations Boundary Value Problems with p-Laplacian Operator[J]. Acta mathematica scientia,Series A, 2021, 41(2): 402-414.

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