{"paper":{"title":"On Dirichlet problem for fractional $p$-Laplacian with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K.Sreenadh, Tuhina Mukherjee","submitted_at":"2016-02-02T10:50:30Z","abstract_excerpt":"In this article, we study the following fractional $p$-Laplacian equation with critical growth singular nonlinearity \\begin{equation*}\n  \\quad (-\\De_{p})^s u = \\la u^{-q} + u^{\\alpha}, u>0 \\; \\text{in}\\; \\Om,\\quad u = 0 \\; \\mbox{in}\\; \\mb R^n \\setminus\\Om. \\end{equation*} where $\\Om$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Om$, $n > sp, s \\in (0,1), \\la >0, 0 < q \\leq 1 $ and $\\alpha\\le p^*_s-1$. We use variational methods to show the existence and multiplicity of positive solutions of above problem with respect to parameter $\\la$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00872","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"}