应用数学2026，Vol.39Issue(3)：651-664,14.
具有次线性项和双临界增长的薛定谔泊松系统规范化解的存在性
Existence of Normalized Solutions to the Schrödinger-Poisson System with Sublinear Terms and Double Critical Growth
摘要
Abstract
This paper investigates the existence of normalized solutions to the Schrödinger-Poisson system with sublinear terms and double critical growth.Due to the presence of Sobolev critical and nonlo-cal critical terms,the energy functional of the system is always unbounded from below.The concentration compactness principle is employed to recover the loss of compactness of the energy functional caused by critical growth.A truncation technique is used to ensure that the truncated functional is bounded from below and coercive.Finally,the multiplicity of normalized solutions is obtained by using the genus theory.By constructing an auxiliary map,which has the same type of geometric structure on S(a)× R as on S(a),and applying the concentration compactness principle,a mountain pass solution with positive energy level is obtained.关键词
薛定谔泊松系统/次线性项/双临界增长/集中紧性/规范化解Key words
Schrödinger-Poisson system/Sublinear terms/Double critical growth/Concentration compactness/Normalized solution分类
数理科学引用本文复制引用
樊再美,张家锋..具有次线性项和双临界增长的薛定谔泊松系统规范化解的存在性[J].应用数学,2026,39(3):651-664,14.基金项目
国家自然科学基金(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-zk[2025]面上 218) （黔科合基础-zk[2025]面上 218）
