Classification and refined singularity of positive solutions for nonlinear Maxwell equations arising in mesoscopic electromagnetism

This paper is a continuation of 13], where we studied the existence and other analytic properties of positive radial solutions for a system of nonlinear Maxwell equations in the plane R²${\mathbb{R}}^2$, which arises in the modelling of mesoscopic scale electromagnetic phenomena. In this paper we derive local estimates of singular positive solutions, based on which a classification theorem of general positive solutions is established. The refined singularity of general positive solutions is also investigated by employing the theory of infinite dimensional dynamical systems.