{"paper":{"title":"Quasilinear and Hessian Lane-Emden type systems with measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laurent V\\'eron (LMPT), Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Quoc-Hung Nguyen (Scuola Normale Superiore)","submitted_at":"2017-05-23T08:55:19Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08136","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}