Kazdan–Warner equation on hypergraphs - Zhang, Haigang; Zhao, Juan (Ukrains’kyi Matematychnyi Zhurnal, 2026)
UDC 519.17. 519.951Let $H=(V, E)$ be a connected finite hypergraph, which is an extension of the graph theory in which the edges may connect more than two vertices and form hyperedges. We study the Kazdan-Warner equation\begin{gather*}Δ φ=c-he^{φ}\end{gather*} on $H,$ where $c$ is a constant and $h$ is a known function defined on $H$. Based on the work by Grigor'yan, Lin, and Yang [A. Grigor'yan, Y. Lin, Y. Yang, Kazdan–Warner equation on graph, Calc. Var. Partial Differential Equations, 55, № 4, Article 92 (2016)], we employ the variational calculus to extend the main results concerning the solutions to the Kazdan-Warner equation from finite graphs to hypergraphs. We obtain similar results for the cases where $c>0$ and $c