Quasilinear and Hessian Lane-Emden type systems with measure data

Abstract

We study nonlinear systems of the form $-\Delta \_pu=v^{q\_1}+\mu ,-\Delta \_pv=u^{q\_2}+\eta$ and $F\_k[-u]=v^{s\_1}+\mu ,F\_k[-v]=u^{s\_2}+\eta$ in a bounded domain $\Omega$ or in ${\mathbb{R}}^N$ where $\mu$ and $\eta$ are nonnegative Radon measures, $\Delta \_p$ 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.

Potential Analysis, to appear. arXiv admin note: text overlap with arXiv:1305.4332