Electron. J. Diff. Equ., Vol. 2016 (2016), No. 09, pp. 1-7.

Non-local elliptic systems on the Heisenberg group

Nasser Al-Salti, Sebti Kerbal

Abstract:
We present Liouville type results for certain systems of nonlinear elliptic equations containing fractional powers of the Laplacian on the Heisenberg group. Our method of proof is based on the test function method and a recent inequality proved by Alsaedi, Ahmad, and Kirane, leading to the derivation of sufficient conditions in terms of space dimension and systems parameters.

Submitted September 13, 2015. Published January 6, 2016.
Math Subject Classifications: 35R03, 35J60, 35D02.
Key Words: Fractional diffusion operator; nonlinear elliptic systems; convexity inequality.

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Nasser Al-Salti
Department of Mathematics and Statistics
Sultan Qaboos University, P.O. Box 36
Al-Khodh 123, Muscat, Oman
email: nalsalti@squ.edu.om
Sebti Kerbal
Department of Mathematics and Statistics
Sultan Qaboos University, P.O. Box 36
Al-Khodh 123, Muscat, Oman
email: skerbal@squ.edu.om

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