Singular Solutions of a Higher Dimensional Nonlinear Maxwell Equation Arising in Mesoscopic Electromagnetism

We construct positive radial and non-radial singular solutions in a refined local version for a nonlinear Maxwell equation arising in mesoscopic electromagnetism. To construct singular solutions, we need to know more detailed asymptotic behavior at the isolated singular point of the prescribed singular solutions. When the dimension \(N=2\), detailed asymptotic behaviors at \(x=0\) of singular solutions were presented in a recent paper. In the present paper, we consider the higher dimensional case \(N\geq 3\). We will see that asymptotic expansions of radial solutions with \(N\geq 3\) are similar to those with \(N=2\), but asymptotic expansions of non-radial solutions with \(N\geq 3\) are different from those with \(N=2\).