Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (6): 1759-1773.

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An Application of Linking Theorem to Degenerative Elliptic Equations

Zhou Yinggao(),Li Zhouxin*()   

  1. School of Mathematical and Statistics, Central South University, Changsha 410083
  • Received:2023-01-05 Revised:2023-04-12 Online:2023-12-26 Published:2023-11-16
  • Supported by:
    Degree and Graduate Education Reform Research Project of Hunan Province(2020JGYB031);Education and Teaching Reform Research Project of Central South University(2020JGB020);Education and Teaching Reform Research Project of Central South University(2022ALK006);Education and Teaching Reform Research Project of Central South University(2022jy069);Hunan Provincial Natural Science Foundation(2023JJ30645)

Abstract:

In this paper, we study a class of degenerative quasilinear elliptic equations with critical exponent. Using a change of variable, we reformulate the equation into a semilinear one, and prove the existence of solutions by employing Lions concentration compactness principle and linking theorem based on cone.

Key words: Elliptic equations, Linking thoerem, Critical exponent

CLC Number: 

  • O177.91
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