Jinguo Zhang, Sub-elliptic systems involving critical Hardy-Sobolev exponents and sign-changing weight functions on Carnot groups
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DOI: 10.23952/jnva.8.2024.2.02
Volume 8, Issue 2, 1 April 2024, Pages 199-231
Abstract. This paper concerns the existence and multiplicity of positive solutions for the following subelliptic singular system on Carnot group:
in
in
on
where is a sub-Laplacian on an arbitrary Carnot group
,
,
is the
-gauge,
,
is a bounded domain in
with smooth boundary
,
,
,
,
,
,
,
satisfying
with
as a critical Hardy-Sobolev exponent in the Stratified Lie context. For suitable assumptions on weight functions
,
, and
, by using the variational methods and Nehari manifold, we prove that the subelliptic system admits at least two positive solutions when parameters pair
belongs to a certain subset of
.
How to Cite this Article:
J. Zhang, Sub-elliptic systems involving critical Hardy-Sobolev exponents and sign-changing weight functions on Carnot groups, J. Nonlinear Var. Anal. 8 (2024), 199-231.