JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 42-46.doi: 10.6040/j.issn.1671-9352.0.2020.542

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Existence of solution for the critical biharmonic equations involving Rellich potentials

JIANG Rui-ting1, ZHAI Cheng-bo2*   

  1. 1. College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China;
    2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China
  • Published:2021-06-03

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Abstract: This paper considers a class of critical biharmonic equations involving Rellich potentials Δ2u-μu/(|x|4)=(|u|2*(s)-2u)/(|x|s)+λf(x,u)in a bounded domain. By mountain pass theorem, the existence of at least a nontrivial solution is obtained.

Key words: Rellich potential, Rellich-Sobolev critical exponent, local Palais-Smale condition, mountain pass theorem

CLC Number: 

  • O175.25
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