{"paper":{"title":"Multiplicity results of fractional-Laplace system with sign-changing and singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sarika Goyal","submitted_at":"2016-07-05T08:54:47Z","abstract_excerpt":"In this article, we study the following fractional-Laplacian system with singular nonlinearity \\begin{equation*} (P_{\\lambda,\\mu}) \\left\\{ \\begin{array}{lr} (-\\Delta)^s u = \\lambda f(x) u^{-q}+ \\frac{\\alpha}{\\alpha+\\beta}b(x) u^{\\alpha-1} w^\\beta\\; \\text{in}\\;\\Omega \\\\ (-\\Delta)^s w = \\mu g(x) w^{-q}+ \\frac{\\beta}{\\alpha+\\beta} b(x) u^{\\alpha} w^{\\beta-1}\\; \\text{in}\\;\\Omega \\\\ \\quad \\quad u, w>0\\;\\text{in}\\;\\Omega, \\quad u = w = 0 \\; \\mbox{in}\\; \\mathbb{R}^n \\setminus\\Omega, \\end{array} \\quad \\right. \\end{equation*} where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary $\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01150","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"}