Quasilinear and Hessian Lane-Emden type systems with measure data

We study nonlinear systems of the form $-\mathrm{\Delta }\mathrm{\_}pu=v^{q\mathrm{\_}1}+\mu ,-\mathrm{\Delta }\mathrm{\_}pv=u^{q\mathrm{\_}2}+\eta$ and $F\mathrm{\_}k[-u]=v^{s\mathrm{\_}1}+\mu ,F\mathrm{\_}k[-v]=u^{s\mathrm{\_}2}+\eta$ in a bounded domain $\mathrm{\Omega }$ or in ${\mathbb{R}}^N$ where $\mu$ and $\eta$ are nonnegative Radon measures, $\mathrm{\Delta }\mathrm{\_}p$ and $F\mathrm{\_}k$ are respectively the $p$-Laplacian and the $k$-Hessian operators and $q\mathrm{\_}1$, $q\mathrm{\_}2$, $s\mathrm{\_}1$ and $s\mathrm{\_}2$ positive numbers. We give necessary and sufficient conditions for existence expressed in terms of Riesz or Bessel capacities.