一类分数阶 $ p$-Kirchhoff 方程多解的存在性

一类分数阶 $ p$-Kirchhoff 方程多解的存在性

Existence of Multiple Solutions for a Fractional $ p$-Kirchhoff Equation

摘要/Abstract

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 92-100.

潘柔¹,陈林^1,^2,^*()

¹伊犁师范大学数学与统计学院新疆伊宁 835000
²伊犁师范大学应用数学研究所新疆伊宁 835000

收稿日期:2024-04-03 修回日期:2024-10-11 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: * 陈林, E-mail:clzj008@163.com
基金资助:
新疆维吾尔自治区自然科学基金(2022D01C459)

Rou Pan¹,Lin Chen^1,^2,^*()

¹School of Mathematics and Statistics, Yili Normal University, Xinjiang Yining 835000
²Institute of Applied Mathematics, Yili Normal University, Xinjiang Yining 835000

Received:2024-04-03 Revised:2024-10-11 Online:2025-02-26 Published:2025-01-08
Supported by:
Natural Science Foundation of Xinjiang Uygur Autonomous Region(2022D01C459)

摘要：

该文通过构造 Nehari 流形与定义相应的纤维映射, 研究了一类分数阶 $p$-Kirchhoff 方程边值问题多解的存在性.

关键词: 分数阶椭圆方程, $p$-Kirchhoff 方程, Nehari 流形

Abstract:

In this paper, by constructing the Nehari manifold and defining the corresponding fibering map, we discuss the existence of multiple solutions for a class of fractional $p$-Kirchhoff equation.

Key words: fractional elliptic equation, the $p$-Kirchhoff equation, Nehari manifold

中图分类号:

O175.2

潘柔, 陈林. 一类分数阶 $ p$-Kirchhoff 方程多解的存在性[J]. 数学物理学报, 2025, 45(1): 92-100.

Rou Pan, Lin Chen. Existence of Multiple Solutions for a Fractional $ p$-Kirchhoff Equation[J]. Acta mathematica scientia,Series A, 2025, 45(1): 92-100.

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