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Sinh-Gordon equations on finite graphs

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arxiv 2406.17166 v2 pith:JMVY36GF submitted 2024-06-24 math.DG math.AP

Linlin Sun This is my paper · ORCID
classification math.DGmath.AP
keywords graphsequationsinh-gordoncasedegreefinitenonzeroprescribed
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In this paper, we focus on the sinh-Gordon equation on graphs. We introduce a uniform a priori estimate to define the topological degree for this equation with nonzero prescribed functions on finite, connected and symmetric graphs. Furthermore, we calculate this topological degree case by case and show several existence results. In particular, we prove that the classical sinh-Gordon equation with nonzero prescribed function is always solvable on such graphs.

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Cited by 1 Pith paper

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

  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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