ABSTRACT
In this work, we study the following sub-elliptic equations on Carnot group with Hardy-type singularity and critical Sobolev–Hardy exponents
where
stands for the sub-Laplacian operator on Carnot group
,
, and
is the critical Sobolev–Hardy exponent, Q is the homogeneous dimension with respect to the dilation
naturally associated with
, d is the natural gauge associated with the fundamental solution of
on
,
and
is the horizontal gradient associated with
. Through variational methods combined with the theory of genus, we prove that our problems admit infinitely many solutions.
Disclosure statement
No potential conflict of interest was reported by the author.