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arXiv · 2409.00646

Liouville Theorem for Lane-Emden Equation on the Heisenberg Group

Hua Chen·Xin Liao
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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.

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Hua Chen, Xin Liao. 2024-09-01. Liouville Theorem for Lane-Emden Equation on the Heisenberg Group. https://arxiv.org/abs/2409.00646

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