{"paper":{"title":"Critical growth fractional elliptic problem with singular nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, Tuhina Mukherjee","submitted_at":"2016-02-25T11:18:37Z","abstract_excerpt":"In this article, we study the following fractional Laplacian equation with critical growth and singular nonlinearity  $$\\quad (-\\Delta)^s u = \\lambda a(x) u^{-q} + u^{2^*_s-1}, \\quad u>0 \\; \\text{in}\\; \\Omega,\\quad u = 0 \\; \\mbox{in}\\; \\mathbb{R}^n \\setminus\\Omega,$$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary $\\partial \\Omega$, $n > 2s,\\; s \\in (0,1),\\; \\lambda >0,\\; 0 < q \\leq 1 $, $\\theta \\leq a(x) \\in L^\\infty(\\Omega)$, for some $\\theta>0$ and $2^*_s=\\frac{2n}{n-2s}$. We use variational methods to show the existence and multiplicity of positive solutions of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07886","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"}