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<p>In this paper, we focus on the sinh-Gordon equations 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.</p>

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Sinh-Gordon equations on finite graphs

  • 期刊论文

  • 发表日期：

    2025年8月23日

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  • Linlin Sun

摘要

In this paper, we focus on the sinh-Gordon equations 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.