{"paper":{"title":"Definition, existence, stability and uniqueness of the solution to a semilinear elliptic problem with a strong singularity at $ u = 0 $","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniela Giachetti, Fran\\c{c}ois Murat, Pedro J. Mart\\'inez-Aparicio","submitted_at":"2016-06-23T10:49:28Z","abstract_excerpt":"In this paper we consider a semilinear elliptic equation with a strong singularity at $u=0$, namely $ \\displaystyle u\\geq 0 \\mbox{ in } \\Omega$, $ \\displaystyle - div \\,A(x) D u = F(x,u) \\mbox{ in} \\; \\Omega$, $u = 0 \\mbox{ on} \\; \\partial \\Omega$, with $F(x,s)$ a Carath\\'eodory function such that $$ 0\\leq F(x,s)\\leq \\frac{h(x)}{\\Gamma(s)}\\,\\,\\mbox{ a.e. } x\\in\\Omega,\\, \\forall s>0, $$ with $h$ in some $L^r(\\Omega)$ and $\\Gamma$ a $C^1([0,+\\infty[)$ function such that $\\Gamma(0)=0$ and $\\Gamma'(s)>0$ for every $s>0$. We introduce a notion of solution to this problem in the spirit of the soluti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07267","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"}