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

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.