Existence and asymptotic analysis of topological solutions for generalized Chern--Simons equations on discrete lattice graphs

Abstract

We study a class of generalized Chern-Simons equations on discrete lattice graphs. By an iterative scheme combined with an exhaustion argument, we establish the existence of topological solutions, which is also the maximal topological solution. We further examine the behavior of the maximal topological solution as the parameter tends to either infinity or zero. The present work extends the results of Hua et al., arXiv:2310.13905 (2023) and Hou and Kong, Calc. Var. Partial Differ. Equ. 64(3), 77 (2025).