对数薛定谔系统解的存在性

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 1092-1104.

对数薛定谔系统解的存在性

张晶^*(), 修明威

哈尔滨师范大学数学科学学院哈尔滨 150025

收稿日期:2025-03-13 修回日期:2025-06-27 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 张晶 E-mail:zhjmath11@163.com
基金资助:
国家自然科学基金(12561040);国家自然科学基金(12061040);黑龙江省省属本科高校基本科研业务费(2025-KYYWF-ZR0124);Basic Scientific Research Project of Provincial Undergraduate Universities in Heilongjiang Province(2025-KYYWF-ZR0124)

Existence of Solutions for Schrödinger Systems with Logarithmic Terms

Jing Zhang^*(), Mingwei Xiu

School of Mathematics, Harbin Normal University, Harbin 150025

Received:2025-03-13 Revised:2025-06-27 Online:2026-06-26 Published:2026-06-16
Contact: Jing Zhang E-mail:zhjmath11@163.com
Supported by:
NSFC(12561040);NSFC(12061040)

摘要/Abstract

摘要：

对数薛定谔系统在物理学中有广泛的应用, 因此研究其解的存在性具有重要的意义. 该文研究了一类带有临界扰动的对数薛定谔系统解的存在性, 即在 Sobolev 临界条件下, 通过构造系统的能量泛函并应用变分方法, 临界点理论和集中紧性原理得到系统基态解的存在性及相应解的性质.

关键词: 对数薛定谔系统, 基态解, 变分方法, 临界扰动

Abstract:

In this paper, we study the existence of solutions for a class of logarithmic Schrödinger systems with critical perturbations. We obtain the existence of ground state solutions by constructing auxiliary functional and applying variational method, critical point theory and concentrated compactness principle.

Key words: logarithmic Schr?dinger system, ground state solution, variational method, critical perturbations.

中图分类号:

O177.91

张晶, 修明威. 对数薛定谔系统解的存在性[J]. 数学物理学报, 2026, 46(3): 1092-1104.

Jing Zhang, Mingwei Xiu. Existence of Solutions for Schrödinger Systems with Logarithmic Terms[J]. Acta mathematica scientia,Series A, 2026, 46(3): 1092-1104.

参考文献 11

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