On topological solutions to a generalized Chern-Simons equation on lattice graphs

2024/10/24 by Songbo Hou, Hou, Songbo, Xiaoqing Kong +1 · 3 citations
Computer Science · Mathematics · #35A01 35A16 35J91 35R02 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.18407

openalex publication_date 2024/10/24 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28

Abstract

For n ≥ 2, consider ℤⁿ as a lattice graph. We explore a generalized Chern-Simons equation on ℤⁿ. 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. \bf519(1), 126787(2023)], as well as those of Hou and Qiao [J. Math. Phys. \bf65(8), 081503(2024)].

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• Topological solutions of generalized Chern-Simons equations on discrete lattice graphs
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