Liouville Theorem for Lane-Emden Equation on the Heisenberg Group

Abstract

This paper establishes some Liouville type results for solutions to the Lane Emden equation on the entire Heisenberg group, both in the stable and stable outside a compact set scenarios.Specifically, we prove that when p is smaller than the Joseph Lundgren exponent and does not equal the Sobolev exponent, 0 is the unique solution that is stable outside a compact set.

There is an error in equation 2.14. For equation 2.14 to hold, the function $u$ should be cylindrical