Liouville type results for semilinear elliptic equation and inequality on pseudo-Hermitian manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917020465889280 |
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| author | Zhao, Biqiang |
| author_facet | Zhao, Biqiang |
| contents | In this paper, we study the semilinear elliptic equation and inequality on pseudo-Hermitian manifolds. In particular, we first obtain a Liouville theorem for the equation $Δ_b u+F(u)=0$ based on a generalized Jerison-Lee's formula. Next, we prove the nonexistence of a positive solution to the inequality $Δ_b u+F(u)\leq 0$ under the volume estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Liouville type results for semilinear elliptic equation and inequality on pseudo-Hermitian manifolds Zhao, Biqiang Analysis of PDEs Differential Geometry In this paper, we study the semilinear elliptic equation and inequality on pseudo-Hermitian manifolds. In particular, we first obtain a Liouville theorem for the equation $Δ_b u+F(u)=0$ based on a generalized Jerison-Lee's formula. Next, we prove the nonexistence of a positive solution to the inequality $Δ_b u+F(u)\leq 0$ under the volume estimate. |
| title | Liouville type results for semilinear elliptic equation and inequality on pseudo-Hermitian manifolds |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2507.09130 |