Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (2): 636-658.doi: 10.1007/s10473-025-0220-9

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ELLIPTIC EQUATION WITH CRITICAL EXPONENT AND DIPOLE POTENTIAL: EXISTENCE AND DECAY ESTIMATES

Yu Su1, Zhisu Liu2,3,*, Senli Liu4   

  1. 1. School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, China;
    2. School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China;
    3. Institute for Advanced Marine Research, China University of Geosciences, Guangzhou 511462, China;
    4. College of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan 411201, China
  • Received:2023-06-07 Revised:2024-04-11 Online:2025-03-25 Published:2025-05-08
  • Contact: *Zhisu Liu, E-mail: liuzhisu@cug.edu.cn
  • About author:Yu Su, E-mail: yusumath@aust.edu.cn;Senli Liu, E-mail: liusl@hnust.edu.cn
  • Supported by:
    Yu Su's research was supported by the Natural Science Research Project of Anhui Educational Committee(2023AH040155). Zhisu Liu's research was supported by the Guangdong Basic and Applied Basic Research Foundation (2023A1515011679; 2024A1515012704) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUG2106211; CUGST2).

Abstract: The paper is concerned with a class of elliptic equation with critical exponent and Dipole potential. More precisely, we make use of the refined Sobolev inequality with Morrey norm to obtain the existence and decay properties of nonnegative radial ground state solutions.

Key words: Dipole potential, decay estimation, Hardy Sobolev critical exponent, Henon Sobolev critical exponent

CLC Number: 

  • 35Q40
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