Liouville Theorem for Lane-Emden Equation on the Heisenberg Group
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910678732767232 |
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| author | Chen, Hua Liao, Xin |
| author_facet | Chen, Hua Liao, Xin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liouville Theorem for Lane-Emden Equation on the Heisenberg Group Chen, Hua Liao, Xin Analysis of PDEs 2020: 35B33, 35J61, 35J70 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. |
| title | Liouville Theorem for Lane-Emden Equation on the Heisenberg Group |
| topic | Analysis of PDEs 2020: 35B33, 35J61, 35J70 |
| url | https://arxiv.org/abs/2409.00646 |