{"paper":{"title":"A Global multiplicity result for a very singular critical nonlocal equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J.Giacomoni, K. Sreenadh, Tuhina Mukherjee","submitted_at":"2018-06-16T01:39:12Z","abstract_excerpt":"In this article, we show the global multiplicity result for the following nonlocal singular problem \\begin{equation*}\n  (P_\\la):\\;\\quad (-\\De)^s u = u^{-q} + \\la u^{{2^*_s}-1}, \\quad 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 $\\partial \\Om$, $n > 2s,\\; s \\in (0,1),\\; \\la >0,\\; q>0$ satisfies $q(2s-1)<(2s+1)$ and $2^*_s=\\frac{2n}{n-2s}$. Employing the variational method, we show the existence of at least two distinct weak positive solutions for $(P_\\la)$ in $X_0$ when $\\la \\in (0,\\La)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06167","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"}