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Liouville-type theorems for sub-elliptic systems involving Δλ-Laplacian

Authors: 

Phuong Le, Anh Tuan Duong, Nhu Thang Nguyen

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 a and for the corresponding system a , a in a, where a and a is a strongly degenerate operator of the form a. Here the functions a, satisfy certain conditions such that a is homogeneous of degree 2 with respect to a group of dilations in a.

We first prove that the scalar inequality has no positive solution provided awhere Q is the homogeneous dimension of a associated to the operator a.

Then, we establish the nonexistence of positive solutions of the corresponding system in one of following cases:

a

a

a

 

Our proofs are based on a maximum principle argument combined with a refinement of Souto's reduction.