Liouville-type theorems for sub-elliptic systems involving Δλ-Laplacian
Liouville-type theorems for sub-elliptic systems involving Δλ-Laplacian
Source title:
Complex Variables and Elliptic Equations, 66(12),
2021
(ISI)
Academic year of acceptance:
2021-2022
Abstract:
We study the Liouville-type theorems for the sub-elliptic inequality and for the corresponding system
,
in
, where
and
is a strongly degenerate operator of the form
. Here the functions
, satisfy certain conditions such that
is homogeneous of degree 2 with respect to a group of dilations in
.
We first prove that the scalar inequality has no positive solution provided where Q is the homogeneous dimension of
associated to the operator
.
Then, we establish the nonexistence of positive solutions of the corresponding system in one of following cases:
Our proofs are based on a maximum principle argument combined with a refinement of Souto's reduction.