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

Abstract

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 there exists a global solution that also qualifies as a topological solution. Our results extend those of Hua et al. [arXiv:2310.13905] and complement the findings of Chao and Hou [J. Math. Anal. Appl. $519$(1), 126787(2023)], as well as those of Hou and Qiao [J. Math. Phys. $65$(8), 081503(2024)].

13 pages