Solutions to a generalized Chern-Simons Higgs model on finite graphs by topological degree

2024/02/03 by Songbo Hou, Hou, Songbo, Wenjie Qiao +1 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #39A12 #46E39 #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Functional Analysis (math.FA) #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2402.01990

openalex publication_date 2024/02/03 · openalex created_date 2024/02/08 · openalex updated_date 2026/07/28

Abstract

Consider a finite connected graph denoted as G=(V, E). This study explores a generalized Chern-Simons Higgs model, characterized by the equation: Δu = λe^u (e^u - 1)^2p+1 + f, where Δ denotes the graph Laplacian, λ is a real number, p is a non-negative integer, and f is a function on V. Through the computation of the topological degree, this paper demonstrates the existence of a single solution for the model. Further analysis of the interplay between the topological degree and the critical group of an associated functional reveals the presence of multiple solutions. These findings extend the work of Li, Sun, Yang (arXiv:2309.12024) and Chao, Hou (J. Math. Anal. Appl. (2023) 126787).

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• Topological solutions of generalized Chern-Simons equations on discrete lattice graphs
• Existence results for Tzitzéica equation via topological degree method on graphs
• Existence theory for elliptic equations of general exponential nonlinearity on finite graphs

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