# MathSciDoc: An Archive for Mathematician ∫

#### Analysis of PDEsmathscidoc:2207.03007

Communications in Mathematical Physics, 377, 613–621, 2020.2
In this paper, we prove two existence results of solutions to mean field equations Δu+e^u=ρδ_0 and Δu=λe^u(e^u−1)+4π\sum_{j=1}^M δ_{p_j} on an arbitrary connected finite graph, where ρ>0 and λ>0 are constants, M is a positive integer, and p_1,…,p_M are arbitrarily chosen distinct vertices on the graph.
@inproceedings{an2020existence,
title={Existence of Solutions to Mean Field Equations on Graphs},
author={An Huang, Yong Lin, and Shing-Tung Yau},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707153951790910567},
booktitle={Communications in Mathematical Physics},
volume={377},
pages={613–621},
year={2020},
}

An Huang, Yong Lin, and Shing-Tung Yau. Existence of Solutions to Mean Field Equations on Graphs. 2020. Vol. 377. In Communications in Mathematical Physics. pp.613–621. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707153951790910567.