论文标题
bogomol'nyi方程的解决方案的存在和独特性
Existence and uniqueness of solutions to Bogomol'nyi equations on graphs
论文作者
论文摘要
令$ g =（v，e）$为连接的有限图。我们研究bogomol'nyi方程\ begin {等式*} ΔU= \ MATHRM {e}^{图，$ n_j $是一个正整数，$ j = 1,2，\ cdots，k $和$δ_{z__ {s}} $是$ z_s $的狄拉克质量。我们为Bogomol'nyi方程的解决方案的存在和独特性获得了必要的条件。
Let $G=(V,E)$ be a connected finite graph. We study the Bogomol'nyi equation \begin{equation*} Δu= \mathrm{e}^{u}-1 +4 π\sum_{s=1}^{k} n_s δ_{z_{s}} \quad \text { on } \quad G, \end{equation*} where $z_1, z_2,\dots, z_k$ are arbitrarily chosen distinct vertices on the graph, $n_j$ is a positive integer, $j=1,2,\cdots, k$ and $δ_{z_{s}}$ is the Dirac mass at $z_s$. We obtain a necessary and sufficient condition for the existence and uniqueness of solutions to the Bogomol'nyi equation.
