一类带扰动的分数阶临界Choquard方程的正规解  

Normalized solutions for a class of fractional critical Choquard equations with perturbation

作　　者：桑彦彬 Yanbin SANG(School of Mathematics,North University of China,Taiyuan 030051,Shanxi,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《山东大学学报（理学版）》2024年第8期48-55,66,共9页Journal of Shandong University(Natural Science)

基　　金：山西省基础研究计划资助项目(202103021224198)。

摘　　要：研究一类分数阶Choquard方程的正规解,其中非线性项包含Hardy-Littlewood-Sobolev临界指数和带参数的质量超临界非局部项,分析Pohozaev流形的性质,建立了上述方程对应能量泛函的Palais-Smale序列的紧性条件。当扰动项的系数充分大时,获得了其正规基态解的存在性。The normalized solutions for a class of fractional Choquard equations are studied,where Hardy-Littlewood-Sobolev critical exponent and mass supercritical nonlocal term with the parameter are contained in nonlinearites.By analyzing the properties of Pohozaev manifold,the compact condition of Palais-Smale sequences for the energy functional corresponding to above equations is established.When the coefficient of perturbation is large enough,the existence of normalized ground state solutions is obtained.

关 键 词：Choquard方程 正规解 分数阶算子 质量超临界 紧性条件 

分 类 号：O175[理学—数学]