{"paper":{"title":"Multiplicity of positive solutions for a fractional Laplacian equations involving critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongying Jiao, Jinguo Zhang, Xiaochun Liu","submitted_at":"2015-02-08T07:20:32Z","abstract_excerpt":"In this paper we deal with the multiplicity of positive solutions to the fractional Laplacian equation\n  \\begin{equation*} (-\\Delta)^{\\frac{\\alpha}{2}} u=\\lambda f(x)|u|^{q-2}u+|u|^{2^{*}_{\\alpha}-2}u, \\quad\\text{in}\\,\\,\\Omega, u=0,\\text{on}\\,\\,\\partial\\Omega,\n  \\end{equation*} where $\\Omega\\subset \\mathbb{R}^{N}(N\\geq 2)$ is a bounded domain with smooth boundary, $0<\\alpha<2$, $(-\\Delta)^{\\frac{\\alpha}{2}}$ stands for the fractional Laplacian operator, $f\\in C(\\Omega\\times\\mathbb{R},\\mathbb{R})$ may be sign changing and $\\lambda$ is a positive parameter. We will prove that there exists $\\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02222","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"}