{"paper":{"title":"Existence of strictly positive solutions for sublinear elliptic problems in bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tomas Godoy, Uriel Kaufmann","submitted_at":"2013-04-17T16:32:43Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded domain in $\\mathbb{R}^{N}$ and let $m$ be a possibly discontinuous and unbounded function that changes sign in $\\Omega$. Let $f:\\left[ 0,\\infty\\right) \\rightarrow\\left[ 0,\\infty\\right) $ be a continuous function such that $k_{1}\\xi^{p}\\leq f\\left(\\xi\\right) \\leq k_{2}\\xi^{p}$ for all $\\xi\\geq0$ and some $k_{1},k_{2}>0$ and $p\\in\\left(0,1\\right) $. We study existence and nonexistence of strictly positive solutions for nonlinear elliptic problems of the form $-\\Delta u=m\\left(x\\right) f\\left(u\\right) $ in $\\Omega$, $u=0$ on $\\partial\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4883","kind":"arxiv","version":2},"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"}