In this paper, we establish the existence of positive solution of a nonlinear subelliptic equation involving the critical Sobolev exponent on the Heisenberg group, which generalizes a result of Brezis and Nirenberg in the Euclidean case.

Keywords:

Heisenberg group, subLapacian, critical Sobolev exponent, extremals Heisenberg group, subLapacian, critical Sobolev exponent, extremals

MSC Classifications:

35J20, 35J60 show english descriptions Variational methods for second-order elliptic equations
Nonlinear elliptic equations 35J20 - Variational methods for second-order elliptic equations
35J60 - Nonlinear elliptic equations

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