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

For n ≥ 2, consider Zn as a lattice graph. We explore a generalized Chern–Simons equation on Zn. 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 (2023) 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).