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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (12): 110-120.doi: 10.6040/j.issn.1671-9352.0.2023.438

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一类含有p-Laplacian算子的带有参数及分数阶导数的分数阶微分方程边值问题唯一正解的存在性

郑艳萍,杨慧*,王文霞   

  1. 太原师范学院数学与统计学院, 山西 晋中 030619
  • 发布日期:2025-12-10
  • 通讯作者: 杨慧(1976— ),女,副教授,硕士,研究方向为泛函分析与微分方程. E-mail:yh3f@163.com
  • 作者简介:郑艳萍(1978— ),女,副教授,硕士,研究方向为算子理论与微分方程. E-mail:zhengyanping2006@126.com*通信作者:杨慧(1976— ),女,副教授,硕士,研究方向为泛函分析与微分方程. E-mail:yh3f@163.com
  • 基金资助:
    国家自然科学基金资助项目(11361047);山西省基础研究计划项目(20210302124529)

The existence of unique positive solution for boundary value problems of fractional differential equations with parameters and derivatives involving p-Laplacian operators

ZHENG Yanping, YANG Hui*, WANG Wenxia   

  1. School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, Shanxi, China
  • Published:2025-12-10

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摘要： 研究一类带有偏差量、分数阶导数及两个参数且边界条件中含有非线性积分项的分数阶p-Laplacian微分方程边值问题唯一正解的存在性。通过使用锥理论与和算子方法, 获得该边值问题存在唯一正解的最大参数存在区间, 并讨论正解对参数的连续依赖性。最后给出两个具体的例子作为所获结论的应用。

关键词: 分数阶微分方程, 边值问题, p-Laplacian算子, 唯一解

Abstract: This paper investigates the existence and uniqueness of positive solution for a class of boundary value problems of p-Laplacian fractional differential equations with a deviation and fractional derivatives involving nonlinear fractional integral terms in the boundary conditions and two parameters. Based on the cone theory and method operators, the maximum parameter interval for the existence of the unique positive solution is obtained and continuous dependence of the unique positive solution on parameters is discussed. Finally, two examples are given to illustrate the main results.

Key words: fractional differential equation, boundary value problem, p-Laplacian operator, unique solution

中图分类号: 

  • O175
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