Non-local elliptic systems on the Heisenberg group

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.

Keywords

• Fractional diffusion operator
• nonlinear elliptic systems
• convexity inequality