{"paper":{"title":"Multiplicity results of fractional $p$-Laplace equations with sign-changing and singular nonlinearity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sarika Goyal","submitted_at":"2016-04-04T10:18:12Z","abstract_excerpt":"In this article, we study the following fractional $p$-Laplacian equation with singular nonlinearity\n  \\begin{equation*}\n  (P_{\\la}) \\left\\{ \\begin{array}{lr} - 2\\int_{\\mb R^n}\\frac{|w(y)-w(x)|^{p-2}(w(y)-w(x))}{|x-y|^{n+ps}}dy = a(x) w^{-q}+ \\la b(x) w^r\\; \\text{in}\\; \\Om \\quad \\quad w>0\\;\\text{in}\\;\\Om, \\quad w = 0 \\; \\mbox{in}\\; \\mb R^n \\setminus\\Om, \\end{array} \\quad \\right. \\end{equation*} where $\\Om$ is a bounded domain in $\\mb R^n$ with smooth boundary $\\partial \\Om$, $n> ps$,$s\\in(0,1)$, $\\la>0$, $0<q<1$, $q<p-1<r< p_{s}^*-1$ with $p_{s}^*=\\frac{np}{n-ps}$, $a: \\Om\\subset\\mb R^n \\ra \\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00801","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"}