海南师范大学学报（自然科学版）2025，Vol.38Issue(3)：264-273,10.DOI:10.12051/j.issn.1674-4942.2025.03.002
含有调和位势和一般非线性项的Choquard方程正规化解的存在性
The Existence of Normalized Solutions for the Choquard Equation with Harmonic Potential and General Nonlinear Terms
摘要
Abstract
The Choquard equation with harmonic potential and general nonlinear terms is an important class of nonlinear partial differential equation and widely applied in quantum mechanics and physics.This paper investigates the existence of normalized solutions for this type of equation,and prove the existence of local minima and mountain pass solutions.Using the variational method,we first construct an energy functional.By analyzing the properties of this energy functional,espe-cially its minimization property in Sobolev spaces,and applying the Palais-Smale condition,we further ensure the exis-tence and smoothness of local minima in appropriate Sobolev spaces through the analysis of the influence of the nonlinear terms and harmonic potential.The existence of mountain pass solution is closely related to the topological properties of the energy functional.By delving into the topological structure of the energy functional and applying refined techniques from variational methods,we further prove the existence of mountain pass solution through the analysis of the specific properties of the nonlinear terms and harmonic potential.This provides the existence of multiple solutions to the equation.The results of this paper are not only of significant mathematical importance but also provide theoretical support for the in-depth analysis of related physical problems,extending the results in the existing literature.关键词
Choquard方程/调和位势/约束变分法/正规化解Key words
Choquard equation/harmonic potential/constrained variational method/normalized solution分类
数理科学引用本文复制引用
樊再美,张家锋..含有调和位势和一般非线性项的Choquard方程正规化解的存在性[J].海南师范大学学报（自然科学版）,2025,38(3):264-273,10.基金项目
国家自然科学基金项目(11861021) （11861021）
贵州省教育厅自然科学研究项目(QJJ2023012,QJJ2023061,QJJ2023062) （QJJ2023012,QJJ2023061,QJJ2023062）
贵州民族大学自然科学研究项目(GZMUZK[2022]YB06) （GZMUZK[2022]YB06）
贵州省基础研究计划项目(黔科合基础MS[2025]218) （黔科合基础MS[2025]218）
