| Contents |
| We are interested in ground states for the nonlinear curl-curl equation
$$
\nabla\times\nabla\times U + V(x) U = \Gamma(x) |U|^{p-1} U \mbox{ in } I\!\!R^3, \quad U: I\!\!R^3\to I\!\!R^3.
$$
A basic requirement is to find scenarios, where $0$ does not belong to the spectrum of the operator
$$
{\mathcal L} = \nabla\times\nabla\times+ V(x).
$$
Under suitable assumptions on $V, \Gamma$ we construct ground states both for the defocusing case ($\Gamma\leq 0$) and the focusing case ($\Gamma\geq 0$). The main tools are variational methods and the use of symmetries. |
|