含参数的p-Laplacian分数阶微分方程多重正解的存在性

兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (1): 166-172.

• 数理科学 • 上一篇

含参数的p-Laplacian分数阶微分方程多重正解的存在性

吴克晴^*, 徐紫钰, 蔡序军

江西理工大学理学院, 江西赣州 341000

收稿日期:2023-03-09 出版日期:2025-02-28 发布日期:2025-03-03
通讯作者: 吴克晴(1972-),男,江西鹰潭人,博士,副教授.Email:wkq622@126.com

Existence of multiple positive solutions for p-Laplacian fractional differential equations with a parameter

WU Ke-qing, XU Zi-yu, CAI Xu-jun

School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China

Received:2023-03-09 Online:2025-02-28 Published:2025-03-03

摘要/Abstract

摘要： 考虑了一类具有p-Laplacian算子同时非线性项含积分项的Riemann-Liouville型非线性分数阶微分方程,分析其在包含参数及分数阶积分条件的边界条件下的多重正解的存在性.利用格林函数将问题转化为积分方程,并在Banach空间中运用Leggett-Williams不动点定理和广义Avery-Henderson不动点定理获得主要结果,通过一个实例说明所得结果的适用性.

关键词: p-Laplacian算子, 参数, 多重正解, 不动点定理

Abstract: A class of nonlinear fractional differential equations of Riemann-Liouville type with p-Laplacian operator and nonlinear terms containing an integral term is considered. The focus is on analyzing its existence of multiple positive solutions under the boundary conditions including a parameter and fractional integral conditions. The problem is transformed into an integral equation by using the Green function. The main results are derived using the Leggett-Williams fixed point theorem and the generalized Avery-Henderson fixed point theorem in the Banach space. The applicability of the result is illustrated by an example.

Key words: p-Laplacian operator, parameter, multiple positive solutions, fixed point theorem

中图分类号:

O175.8

吴克晴, 徐紫钰, 蔡序军. 含参数的p-Laplacian分数阶微分方程多重正解的存在性[J]. 兰州理工大学学报, 2025, 51(1): 166-172.

WU Ke-qing, XU Zi-yu, CAI Xu-jun. Existence of multiple positive solutions for p-Laplacian fractional differential equations with a parameter[J]. Journal of Lanzhou University of Technology, 2025, 51(1): 166-172.

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含参数的p-Laplacian分数阶微分方程多重正解的存在性

Existence of multiple positive solutions for p-Laplacian fractional differential equations with a parameter

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