On a critical curl-curl system of Lane-Emden type

We study the system $\nabla\times\nabla\times u = |v|^{q-2}v$, $\nabla\times\nabla\times v = |u|^{p-2}u$ of Lane-Emden type in $\mathbb R^3$, with exponents $p,q>3$ on the critical hyperbola $1/p+1/q=1/3$. We prove the existence of a ground state solution by reducing the system to a quasilinear four