Quasilinear and Hessian Lane-Emden type systems with measure data

Abstract

We study nonlinear systems of the form $-Δ\_pu=v^{q\_1}+μ,\;-Δ\_pv=u^{q\_2}+η$ and $F\_k[-u]=v^{s\_1}+μ,\;F\_k[-v]=u^{s\_2}+η$ in a bounded domain $Ω$ or in $\mathbb{R}^N$ where $μ$ and $η$ are nonnegative Radon measures, $Δ\_p$ and $F\_k$ are respectively the $p$-Laplacian and the $k$-Hessian operators and $q\_1$, $q\_2$, $s\_1$ and $s\_2$ positive numbers. We give necessary and sufficient conditions for existence expressed in terms of Riesz or Bessel capacities.