中山大学学报（自然科学版）（中英文）2025，Vol.64Issue(2)：138-147,10.DOI:10.13471/j.cnki.acta.snus.ZR20240032
一类带有对数项的临界Choquard方程组的基态解
Ground state solutions of a class of critical Choquard systems with logarithmic terms
摘要
Abstract
A class of Choquard type coupled systems are considered,where Hardy-Littlewood-Sobolev critical exponents and logarithmic terms are contained in nonlinear terms.If the coefficients of logarithmic terms are both negative,Palais-Smale sequences of the energy functional corresponding to above problems in Nehari manifold are established by using of the existence on a local minima of single critical Choquard equation.Furthermore,by adopting Ekeland's variational principle,some restricted conditions under which the parameters are related to the first eigenvalue of linear operator with Dirichlet boundary conditions are given.The nonnegative solution with negative energy level of above systems is obtained.Our work generalizes the cases that the coefficients of logarithmic terms are positive,and analyzes the impact of negative coefficients on geometry structure of the energy functional.In fact,our results extend classical Sobolev critical systems to the corresponding Choquard problems.关键词
Choquard型系统/对数项/基态解/临界指数/耦合项Key words
Choquard systems/logarithmic terms/ground state solutions/critical exponents/coupled terms分类
数理科学引用本文复制引用
桑彦彬,蔚艳,史娜..一类带有对数项的临界Choquard方程组的基态解[J].中山大学学报（自然科学版）（中英文）,2025,64(2):138-147,10.基金项目
山西省基础研究计划(202103021224198) （202103021224198）
山西省科技战略研究专项(202304031401075) （202304031401075）
