{"paper":{"title":"Three nontrivial solutions of a nonlocal problem involving critical exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amita Soni, D.Choudhuri","submitted_at":"2018-12-04T10:56:30Z","abstract_excerpt":"In this paper we will prove the existence of three nontrivial weak solutions of the following problem involving a nonlinear integro-differential operator and a term with critical exponent. \\begin{align*} \\begin{split} -\\mathscr{L}_\\Phi u & = |u|^{{p_{s}^{\\ast}}-2}u+\\lambda f(x,u)\\,\\,\\mbox{in}\\,\\,\\Omega,\\\\ u & = 0\\,\\, \\mbox{in}\\,\\, \\mathbb{R}^N\\setminus \\Omega, \\end{split} \\end{align*} Here $q\\in(p, p_s^*)$, where $p_s^*$ is the fractional Sobolev conjugate of $p$ and $-\\mathscr{L}_\\Phi $ represents a general nonlocal integro-differential operator of order $s\\in(0,1)$. This operator is possibly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01327","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"}