On topological solutions to a generalized Chern-Simons equation on lattice graphs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910706759106560 |
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| author | Hou, Songbo Kong, Xiaoqing |
| author_facet | Hou, Songbo Kong, Xiaoqing |
| contents | For $n \geq 2$, consider $\mathbb{Z}^n$ as a lattice graph. We explore a generalized Chern-Simons equation on $\mathbb{Z}^n$. Employing the method of exhaustion, we prove that there exists a global solution that also qualifies as a topological solution. Our results extend those of Hua et al. [arXiv:2310.13905] and complement the findings of Chao and Hou [J. Math. Anal. Appl. $\bf{519}$(1), 126787(2023)], as well as those of Hou and Qiao [J. Math. Phys. $\bf{65}$(8), 081503(2024)]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_18407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On topological solutions to a generalized Chern-Simons equation on lattice graphs Hou, Songbo Kong, Xiaoqing Analysis of PDEs Functional Analysis 35A01 35A16 35J91 35R02 For $n \geq 2$, consider $\mathbb{Z}^n$ as a lattice graph. We explore a generalized Chern-Simons equation on $\mathbb{Z}^n$. Employing the method of exhaustion, we prove that there exists a global solution that also qualifies as a topological solution. Our results extend those of Hua et al. [arXiv:2310.13905] and complement the findings of Chao and Hou [J. Math. Anal. Appl. $\bf{519}$(1), 126787(2023)], as well as those of Hou and Qiao [J. Math. Phys. $\bf{65}$(8), 081503(2024)]. |
| title | On topological solutions to a generalized Chern-Simons equation on lattice graphs |
| topic | Analysis of PDEs Functional Analysis 35A01 35A16 35J91 35R02 |
| url | https://arxiv.org/abs/2410.18407 |