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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (8): 48-55,66.doi: 10.6040/j.issn.1671-9352.0.2023.543

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一类带扰动的分数阶临界Choquard方程的正规解

桑彦彬()   

  1. 中北大学数学学院, 山西 太原 030051
  • 收稿日期:2023-12-25 出版日期:2024-08-20 发布日期:2024-07-31
  • 作者简介:桑彦彬(1979—)，男，副教授，硕士生导师，博士，研究方向为非线性泛函分析及非线性微分方程. E-mail: sangyanbin@126.com
  • 基金资助:
    山西省基础研究计划资助项目(202103021224198)

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

Yanbin SANG()   

  1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
  • Received:2023-12-25 Online:2024-08-20 Published:2024-07-31

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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。

关键词: Choquard方程, 正规解, 分数阶算子, 质量超临界, 紧性条件

Abstract:

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.

Key words: Choquard equation, normalized solution, fractional operator, mass supercritical, compact condition

中图分类号: 

  • O175
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