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

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arxiv 2410.18407 v2 pith:5REOHHSX submitted 2024-10-24 math.AP math.FA

Songbo Hou , Xiaoqing Kong This is my paper · ORCID
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abstract

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)].

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On finite-energy solutions of Kazan-Warner equations on the lattice graph

    math.AP 2025-09 unverdicted novelty 8.0 of 10

    Finite-energy solutions exist for Kazdan-Warner type equations on the square lattice for small κ, partially resolving an open problem for the lattice Liouville equation.

  2. Existence theory for elliptic equations of general exponential nonlinearity on finite graphs

    math.AP 2025-05 reject novelty 6.0 of 10

    A sign error in the graph-reduction step invalidates the claimed Brouwer degree formula and the existence theory built on it.

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