Chern–Simons Higgs models for  <i>p</i> -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.