Ground and Bound State Solutions of Semilinear Time-Harmonic Maxwell Equations in a Bounded Domain

We find solutions E : Omega -> R-3 of the problem {del x (del x E) + gimel E = partial derivative F-E(x, E) in Omega v x E = 0 on partial derivative Omega on a simply connected, smooth, bounded domain Omega subset of R-3 with connected boundary and exterior normal nu : partial derivative Omega -> R-3. Here denotes del x the curl operator in R-3, the nonlinearity F : Omega x R-3 -> R-3 is superquadratic and subcritical in E. The model nonlinearity is of the form F(x, E) = Gamma(x)vertical bar E vertical bar(p) for Gamma is an element of L-infinity (Omega) positive, some 2 < p < 6. It need not be radial nor even in the E-variable. The problem comes from the time-harmonic Maxwell equations, the boundary conditions are those for Omega surrounded by a perfect conductor.