带有双幂非线性项的 $L^2$-次临界变分问题的极小元性质——献给邓引斌教授 70 寿辰

数学物理学报 ›› 2026, Vol. 46 ›› Issue (4): 1309-1319.

带有双幂非线性项的 $L^2$-次临界变分问题的极小元性质——献给邓引斌教授 70 寿辰

郭玉劲¹(), 张姝²^,^*()

¹ 华中师范大学数学与统计学学院武汉 430079
² 信阳师范大学数学与统计学院河南信阳 464000

收稿日期:2025-08-27 修回日期:2025-11-21 出版日期:2026-08-26 发布日期:2026-06-10
通讯作者: 张姝 E-mail:yguo@ccnu.edu.cn;szhangmath@163.com
作者简介:郭玉劲,E-mail: yguo@ccnu.edu.cn
基金资助:
国家自然科学基金(12225106);国家自然科学基金(12326338);国家自然科学基金(12526559);科技部国家重点研发项目(2023YFA1010001)

Minimizers of $L^2$-Subcritical Constraint Variational Problems with Double-Power Nonlinear Terms

Yujin Guo¹(), Shu Zhang²^,^*()

¹ School of Mathematics and Statistics, Central China Normal University, Wuhan 430079
² School of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000

Received:2025-08-27 Revised:2025-11-21 Online:2026-08-26 Published:2026-06-10
Contact: Shu Zhang E-mail:yguo@ccnu.edu.cn;szhangmath@163.com
Supported by:
NSFC(12225106);NSFC(12326338);NSFC(12526559);National Key R & D Program of China(2023YFA1010001)

摘要/Abstract

摘要：

该文主要研究一类带有双幂非线性项的 $L^2$-次临界约束变分问题极小元的性质. 应用紧性引理和一些重要的不等式, 该文首先证明极小元的存在性. 在此基础上, 采用能量方法和爆破分析等理论与方法, 在粒子之间的相互吸引力强度 $\alpha$ 满足 $\alpha\to\infty$ 时, 该文进一步分析正极小元的极限行为.

关键词: 双幂非线性项, 极小元, 存在性, 极限行为

Abstract:

This paper mainly studies the properties of minimizers for $L^2$-subcritical constrained variational problems with double-power nonlinear terms. Applying the compactness lemma and some important inequalities, we first prove the existence of minimizers. Based on this, using energy method, blow-up argument and some other methods, we further analyze the limiting behavior of positive minimizers as the attractive strength $\alpha$ among the particles tends to infinity.

Key words: double-power nonlinear terms, minimizers, existence, limiting behavior

中图分类号:

O177.91

郭玉劲, 张姝. 带有双幂非线性项的 $L^2$-次临界变分问题的极小元性质——献给邓引斌教授 70 寿辰[J]. 数学物理学报, 2026, 46(4): 1309-1319.

Yujin Guo, Shu Zhang. Minimizers of $L^2$-Subcritical Constraint Variational Problems with Double-Power Nonlinear Terms[J]. Acta mathematica scientia,Series A, 2026, 46(4): 1309-1319.

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