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Existence of solutions to a generalized self-dual Chern-Simons system on finite graphs

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arxiv 2206.12863 v1 pith:HOJOP6VG submitted 2022-06-26 math.AP

Ruixue Chao , Songbo Hou , Jiamin Sun This is my paper · ORCID
classification math.AP
keywords solutionscasechern-simonsexistencefinitegraphssystemanalysis
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We study a system of equations arising in the Chern-Simons model on finite graphs. Using the iteration scheme and the upper and lower solutions method, we get existence of solutions in the non-critical case. The critical case is dealt with by priori estimates. Our results generalize those of Huang et al. (Journal of Functional Analysis 281(10) (2021) Paper No. 109218).

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  1. 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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