Geodesic
Liouville type theorems for subelliptic systems on the Heisenberg group with general nonlinearity
Vishvesh Kumar1 ; Michael Ruzhansky1 ; Rong Zhang2
1 Ghent University, Department of Mathematics: Analysis, Logic and Discrete Mathematics
2 Chinese Academy of Sciences, HLM, Academy of Mathematics and Systems Science, and Ghent University, Department of Mathematics: Analysis, Logic and Discrete Mathematics
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 561–582.

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In this paper, we establish Liouville type results for semilinear subelliptic systems associated with the sub-Laplacian on the Heisenberg group $\mathbb{H}^{n}$ involving two different kinds of general nonlinearities. The main technique of the proof is the method of moving planes combined with some integral inequalities replacing the role of maximum principles. As a special case, we obtain the Liouville theorem for the Lane–Emden system on the Heisenberg group $\mathbb{H}^{n}$, which also appears to be a new result in the literature.
DOI : 10.54330/afm.148660
Keywords: Liouville-type theorem, Lane–Emden system, method of moving plane, Heisenberg group, semilinear subelliptic systems, integral inequalities

Vishvesh Kumar 1 ; Michael Ruzhansky 1 ; Rong Zhang 2

1 Ghent University, Department of Mathematics: Analysis, Logic and Discrete Mathematics
2 Chinese Academy of Sciences, HLM, Academy of Mathematics and Systems Science, and Ghent University, Department of Mathematics: Analysis, Logic and Discrete Mathematics 
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Vishvesh Kumar; Michael Ruzhansky; Rong Zhang. Liouville type theorems for subelliptic systems on the Heisenberg group with general nonlinearity. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 561–582. doi : 10.54330/afm.148660. http://geodesic.mathdoc.fr/articles/10.54330/afm.148660/

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