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We consider the nonlinear curl-curl problem $\nabla\times\nabla\times U +V(x) U=f(x,|U|^2)U$ in $\mathbb{R}^3$ related to the nonlinear Maxwellequations with Kerr-type nonlinear material laws. We prove the existence of asymmetric ground-state type solution for a bounded, cylindrically symmetriccoefficient $V$ and subcritical cylindrically symmetric nonlinearity $f$. Thenew existence result extends the class of problems for which ground-state typesolutions are known. It is based on compactness properties of symmetricfunctions due to Lions, new rearrangement type inequalities from Brock and therecent extension of the Nehari-manifold technique by Szulkin and Weth.

Existence of cylindrically symmetric ground states to a nonlinear curl-curl equation with non-constant coefficients