含非齐次项的薛定谔方程基态解的存在性和集中行为——献给邓引斌教授 70 寿辰

数学物理学报 ›› 2026, Vol. 46 ›› Issue (4): 1420-1427.

含非齐次项的薛定谔方程基态解的存在性和集中行为——献给邓引斌教授 70 寿辰

巴娜¹(), 周凯瑞²(), 曾小雨²^,^*()

¹ 湖北工业大学理学院武汉 430068
² 武汉理工大学数学与统计学院武汉 430070

收稿日期:2025-12-25 修回日期:2026-02-06 出版日期:2026-08-26 发布日期:2026-06-10
通讯作者: 曾小雨 E-mail:bana1002@126.com;zkr_20060222@qq.com;xyzeng@whut.edu.cn
作者简介:巴娜, E-mail: bana1002@126.com;
周凯瑞, zkr_20060222@qq.com
基金资助:
湖北省教育厅科研项目重点项目(D20181405);国家自然科学基金(12322106);国家自然科学基金(12171379)

On the Existence and Concentration of Minimizers for a Class of Constrained Variational Problems in Three Dimensional Space

Na Ba¹(), Kairui Zhou²(), Xiaoyu Zeng²^,^*()

¹ School of Science, Hubei University of Technology, Wuhan 430068
² School of Mathematics and Statistics, Wuhan University of Technology, Wuhan 430070

Received:2025-12-25 Revised:2026-02-06 Online:2026-08-26 Published:2026-06-10
Contact: Xiaoyu Zeng E-mail:bana1002@126.com;zkr_20060222@qq.com;xyzeng@whut.edu.cn
Supported by:
Key Scientific Research Project of Hubei Provincial Department of Education(D20181405);NSFC(12322106);NSFC(12171379)

摘要/Abstract

摘要：

该文利用约束变分的方法, 研究了三维空间中一类带有非齐次项的薛定谔方程存在基态解的最佳参数范围, 并讨论了基态解随参数变化的质量集中行为.

关键词: 约束变分, 基态解, 能量估计, 集中行为

Abstract:

In this paper, we employ the constrained variational method to investigate the optimal parameter range for the existence and non-existence of ground states to a class of Schrödinger equations with inhomogeneous terms in three-dimensional space, and discusses the mass concentration behavior of the ground states with respect to the variation of the parameter.

Key words: constrained variation, ground states, energy estimation, concentration behavior

中图分类号:

O175.25

巴娜, 周凯瑞, 曾小雨. 含非齐次项的薛定谔方程基态解的存在性和集中行为——献给邓引斌教授 70 寿辰[J]. 数学物理学报, 2026, 46(4): 1420-1427.

Na Ba, Kairui Zhou, Xiaoyu Zeng. On the Existence and Concentration of Minimizers for a Class of Constrained Variational Problems in Three Dimensional Space[J]. Acta mathematica scientia,Series A, 2026, 46(4): 1420-1427.

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