Stable solutions to the Maxwell-Chern-Simons model

Abstract

In this paper, we consider an elliptic system arising from the study of the Maxwell-Chern-Simons model, which involves two distinct parameters: the Chern-Simons mass scale μ and the inverse Chern-Simons parameter λ. We first establish the equivalence between stable solutions and topological solutions with respect to the two distinct parameters in the Chern-Simon type regime. To address stability of our elliptic system, we study a reduced functional involving the Laplacian, and biharmonic terms appear in the corresponding linearized operator of the second Fréchet derivative. So, meticulous analysis is required to handle the biharmonic terms as well as the disparate scales of the two parameters. Furthermore, we show the uniqueness of stable solutions in the Chern-Simon type regime.