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

TL;DR

This paper proves the existence and analyzes the asymptotic behavior of topological solutions for generalized Chern-Simons equations on discrete lattice graphs, extending previous results.

Contribution

It introduces an iterative and exhaustion method to establish the existence of maximal topological solutions and studies their asymptotic limits.

Findings

Existence of topological solutions on discrete lattice graphs.

Identification of the maximal topological solution.

Asymptotic behavior as parameters tend to zero or infinity.

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).