{"paper":{"title":"Positive solutions to a fractional equation with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adimurthi, Jacques Giacomoni, Sanjiban Santra","submitted_at":"2017-06-06T20:35:32Z","abstract_excerpt":"In this paper, we study the positive solutions to the following singular and non local elliptic problem posed in a bounded and smooth domain $\\Omega\\subset \\R^N$, $N> 2s$: % \\begin{eqnarray*} (P_\\lambda)\\left\\{\\begin{array}{lll} &(-\\Delta)^s u=\\lambda(K(x)u^{-\\delta}+f(u))\\mbox{ in }\\Omega &u>0 \\mbox{ in }\\Omega & u\\equiv\\, 0\\mbox{ in }\\R^N\\backslash\\Omega. \\end{array}\\right. \\end{eqnarray*} % Here $0<s<1$, $\\delta>0$, $\\lambda>0$ and $f\\,:\\, \\R^+\\to\\R^+$ is a positive $C^2$ function. $K\\,:\\, \\Omega\\to \\R^+$ is a H\\\"older continuous function in $\\Omega$ which behave as ${\\rm dist}(x,\\partial\\O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01965","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"}