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In this paper, we show the nonexistence results for the Kirchhoff elliptic,parabolic, and hyperbolic type equations on the Heisenberg groups. Also, thepseudo-parabolic and pseudo-hyperbolic equations of the Kirchhoff-type areunder consideration. To prove these results we use the test function method. Inaddition, the analogous results are transferred to the cases of systems. Also,we give some examples of non-local nonlinearities.

Liouville theorems for Kirchhoff-type hypoelliptic Partial Differential Equations and systems. I. Heisenberg group