  We find solutions $E:\Omega\to\mathbb{R}^3$ of the problem \[
\left\{\begin{aligned} &\nabla\times(\nabla\times E) + \lambda E = \partial_E
F(x,E) &&\quad \text{in}\Omega\\ &\nu\times E = 0 &&\quad
\text{on}\partial\Omega \end{aligned} \right. \] on a simply connected, smooth,
bounded domain $\Omega\subset\mathbb{R}^3$ with connected boundary and exterior
normal $\nu:\partial\Omega\to\mathbb{R}^3$. Here $\nabla\times$ denotes the
curl operator in $\mathbb{R}^3$, the nonlinearity
$F:\Omega\times\mathbb{R}^3\to\mathbb{R}$ is superquadratic and subcritical in
$E$. The model nonlinearity is of the form $F(x,E)=\Gamma(x)|E|^p$ for
$\Gamma\in L^\infty(\Omega)$ 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.
