{"paper":{"title":"Wiener criteria for existence of large solutions of quasilinear elliptic equations with absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hung Nguyen Quoc (LMPT), Laurent Veron (LMPT)","submitted_at":"2013-08-13T19:41:55Z","abstract_excerpt":"We obtain sufficient conditions expressed in terms of Wiener type tests involving Hausdorff or Bessel capacities for the existence of large solutions to equations (1) $-\\Gd_pu+e^{\\lambda u}+\\beta=0$ or (2) $-\\Gd_pu+\\lambda |u|^{q-1}u+\\beta=0$ in a bounded domain $\\Gw$ when $q>p-1>0, \\lambda>0$ and $\\beta\\in\\mathbb{R}$. We apply our results to equations (3) $-\\Gd_pu+a\\abs{\\nabla u}^{q}+bu^{s}=0$, (4) $\\Gd_p u+u^{-\\gamma}=0$ with $10, b\\geq 0$ and $(q-p+1)+b(s-p+1)>0$, $\\gamma>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2956","kind":"arxiv","version":4},"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"}