一类分数阶 $ p$-Kirchhoff 方程多解的存在性

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

一类分数阶 $ p$-Kirchhoff 方程多解的存在性

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)

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

Pan Rou¹,Chen Lin^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/Abstract

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.

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

[1]	张潇, 张宏武. 分数阶椭圆方程反边值问题的分数 Tikhonov 正则化方法[J]. 数学物理学报, 2024, 44(4): 978-993.
[2]	张文丽, 钟立楠. R^N中一类(p, q)-Laplacian椭圆方程组的多重正解[J]. 数学物理学报, 2014, 34(5): 1264-1274.
[3]	张文丽, 钟立楠. R^N中一类拟线性椭圆方程组非负解的存在性和多重性[J]. 数学物理学报, 2013, 33(1): 174-184.
[4]	魏公明. 耦合非线性Schrödinger方程组的Neumann问题[J]. 数学物理学报, 2009, 29(5): 1398-1414.