{"paper":{"title":"Existence of three positive solutions for a nonlocal singular dirichlet boundary problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacques Giacomoni, Konijeti Sreenadh, Tuhina Mukherjee","submitted_at":"2018-01-19T15:28:06Z","abstract_excerpt":"In this article, we prove the existence of at least three positive solutions for the following nonlocal singular problem \\begin{equation*} (P_\\la)\\left\\{ \\begin{split} (-\\De)^su &= \\la\\frac{f(u)}{u^q}, \\; \\; u>0 \\;\\; \\text{in}\\;\\; \\Om,\\\\ u &= 0\\;\\; \\text{in}\\;\\; \\mb R^n \\setminus \\Om \\end{split} \\right. \\end{equation*} where $(-\\De)^s$ denotes the fractional Laplace operator for $s\\in (0,1)$, $n>2s$, $q \\in (0,1)$, $\\la>0$ and $\\Om$ is smooth bounded domain in $\\mb R^n$. Here $f :[0,\\infty) \\to [0,\\infty)$ is a continuous nondecreasing map satisfying $\\lim\\limits_{u\\to \\infty}\\frac{f(u)}{u^{q+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06461","kind":"arxiv","version":1},"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"}