On topological solutions to a generalized Chern-Simons equation on lattice graphs

Songbo Hou, Xiaoqing Kong

For $n\ge 2$, consider ${\mathbb{Z}}^n$ as a lattice graph. We explore a generalized Chern-Simons equation on ${\mathbb{Z}}^n$. Employing the method of exhaustion, we prove that ther…