Schrödinger-Bopp-Podolsky-Proca 系统——献给陈化教授 70 寿辰

数学物理学报 ›› 2026, Vol. 46 ›› Issue (2): 751-769.

Schrödinger-Bopp-Podolsky-Proca 系统——献给陈化教授 70 寿辰

鲍佳晴¹(), 陈南博¹^,^*(), 刘晓春²(), 梁赛男²()

¹ 桂林电子科技大学数学与计算科学学院广西桂林 541004
² 武汉大学数学与统计学院武汉 430072

收稿日期:2026-01-14 修回日期:2026-02-02 出版日期:2026-04-26 发布日期:2026-04-27
通讯作者: 陈南博 E-mail:18155929548@163.com;flyingnb@126.com;xcliu@whu.edu.cn;snliang365@163.com
作者简介:鲍佳晴, Email：18155929548@163.com
刘晓春, Email：xcliu@whu.edu.cn
梁赛男, Email：snliang365@163.com
基金资助:
广西自然科学基金(2023GXNSFBA026197);国家大学生创新训练项目(202410595034);国家自然科学基金(12131017);国家自然科学基金(12071364)

On the Schrödinger-Bopp-Podolsky-Proca System with Singular Nonlinearity on Closed Manifolds

Jiaqing Bao¹(), Nanbo Chen¹^,^*(), Xiaochun Liu²(), Sainan Liang²()

¹ School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guangxi Guilin 541004
² School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received:2026-01-14 Revised:2026-02-02 Online:2026-04-26 Published:2026-04-27
Contact: Nanbo Chen E-mail:18155929548@163.com;flyingnb@126.com;xcliu@whu.edu.cn;snliang365@163.com
Supported by:
Guangxi Natural Science Foundation(2023GXNSFBA026197);National College Student Innovation Training Program(202410595034);NSFC(12131017);NSFC(12071364)

摘要/Abstract

摘要：

该文研究了 $3$ 维闭黎曼流形上一类静电型 Schrödinger-Bopp-Podolsky-Proca 系统. 该系统耦合了一个带有奇异非线性项 $u^{-r}$ $(r>0)$ 的 Schrödinger 方程和一个四阶椭圆方程. 作者利用 $\varepsilon$- 正则化技巧与变分方法, 分别在吸引耦合与排斥耦合情形下得到了该系统正解的存在性、唯一性及多重性结果.

关键词: Schrödinger-Bopp-Podolsky-Proca 系统, 奇异性, 变分方法, 黎曼流形

Abstract:

In this paper, we study a Schrödinger-Bopp-Podolsky-Proca system with singular nonlinear terms in the context of closed 3-dimensional manifolds. Employing the $\varepsilon$-approximation techniques and variational methods, we establish the existence, uniqueness, and multiplicity of positive solutions, subject to appropriate conditions.

Key words: Schrödinger-Bopp-Podolsky-Proca system, singularity, variational methods, Riemannian manifold

中图分类号:

O175.29

鲍佳晴, 陈南博, 刘晓春, 梁赛男. Schrödinger-Bopp-Podolsky-Proca 系统——献给陈化教授 70 寿辰[J]. 数学物理学报, 2026, 46(2): 751-769.

Jiaqing Bao, Nanbo Chen, Xiaochun Liu, Sainan Liang. On the Schrödinger-Bopp-Podolsky-Proca System with Singular Nonlinearity on Closed Manifolds[J]. Acta mathematica scientia,Series A, 2026, 46(2): 751-769.

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