Chern-Simons Higgs models for p-Laplacian on finite graphs: a topological degree approach

TL;DR

This paper studies Chern-Simons Higgs models involving p-Laplacian operators on finite graphs, using topological degree theory to address nonlinear challenges and establish existence results.

Contribution

It introduces a novel topological degree approach to analyze nonlinear p-Laplacian models on finite graphs, overcoming previous computational difficulties.

Findings

Established the existence of solutions for the models.

Developed a general method for calculating topological degree.

Addressed nonlinear p-Laplacian challenges on finite graphs.

Abstract

We investigate the Chern-Simons Higgs models for p-Laplacian on a connected finite graph, employing topological degree theory as our main tool. Notably, we overcome the difficulties arising from the nonlinearity of p-Laplacian operator and calculate the corresponding topological degree through a more general approach.