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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.
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Submitted on : Saturday, December 15, 2018 - 11:28:49 PM
Last modification on : Friday, February 19, 2021 - 4:10:03 PM
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  • HAL Id : hal-01525487, version 3
  • ARXIV : 1705.08136

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Marie-Françoise Bidaut-Véron, Quoc-Hung Nguyen, Laurent Véron. Quasilinear and Hessian Lane-Emden type systems with measure data. Potential Analysis, Springer Verlag, 2020, 52, pp.615-643. ⟨hal-01525487v3⟩

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