Ground States of Time-Harmonic Semilinear Maxwell Equations in with Vanishing Permittivity

We investigate the existence of solutions of the time-harmonic semilinear Maxwell equation where , almost everywhere on , denotes the curl operator in and is a nonlinear function in E. In particular we find a ground state solution provided that suitable growth conditions on F are imposed and the -norm of V is less than the best Sobolev constant. In applications, F is responsible for the nonlinear polarization and where mu > 0 is the magnetic permeability, omega is the frequency of the time-harmonic electric field and is the linear part of the permittivity in an inhomogeneous medium.