On Solutions for Singular Toda System on Riemann Surfaces with Boundary
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912400268066816 |
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| author | Hu, Zhengni |
| author_facet | Hu, Zhengni |
| contents | This paper studies solutions to a singular $SU(3)$ Toda system with linear source terms on a compact Riemann surface $Σ$ with smooth boundaries $\partialΣ$. We establish the existence of solutions when the parameters are not critical, assuming that Euler characteristic $χ(Σ)<1$ via analyzing the sublevels. Furthermore, we find a sufficient condition that ensures multiple solutions for generic potentials by Morse inequalities and a transversality theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14979 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Solutions for Singular Toda System on Riemann Surfaces with Boundary Hu, Zhengni Analysis of PDEs 35J50 (Primary) 35J61, 35R01, 58J32 (Secondary) This paper studies solutions to a singular $SU(3)$ Toda system with linear source terms on a compact Riemann surface $Σ$ with smooth boundaries $\partialΣ$. We establish the existence of solutions when the parameters are not critical, assuming that Euler characteristic $χ(Σ)<1$ via analyzing the sublevels. Furthermore, we find a sufficient condition that ensures multiple solutions for generic potentials by Morse inequalities and a transversality theorem. |
| title | On Solutions for Singular Toda System on Riemann Surfaces with Boundary |
| topic | Analysis of PDEs 35J50 (Primary) 35J61, 35R01, 58J32 (Secondary) |
| url | https://arxiv.org/abs/2408.14979 |