Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (3): 478-490.

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The Existence Theorem for a Qusi-Linear Elliptic Equations Involving Critical Sobolev Exponent on the Heisenberg Group

Liu Lijing, Liu Xiaochun   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072
  • Received:2016-09-12 Revised:2017-01-13 Online:2017-06-26 Published:2017-06-26
  • Supported by:
    Supported by the NSFC (11171261, 11371282)

Abstract: In this paper, we study the partial differential equations on the Heisenberg group with a singular potential and critical Sobolev exponent. With the help of Nehari manifold, we prove that our problem has at least one or two positive solutions under different conditions. The result generalized the corresponding result in Euclidean space.

Key words: Heisenberg group, Nehari manifoid, Critical Sobolev exponent

CLC Number: 

  • O175.2
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