{"paper":{"title":"Fractional Choquard Equation with Critical Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, Tuhina Mukherjee","submitted_at":"2016-05-22T15:32:23Z","abstract_excerpt":"In this article, we study the Brezis-Nirenberg type problem of nonlinear Choquard equation involving a fractional Laplacian \\[ (-\\De)^s u = \\left( \\int_{\\Om}\\frac{|u|^{2^*_{\\mu,s}}}{|x-y|^{\\mu}}\\mathrm{d}y \\right)|u|^{2^*_{\\mu,s}-2}u +\\la u \\; \\text{in } \\Om,\\] where $\\Om $ is a bounded domain in $\\mathbb R^n$ with Lipschitz boundary, $\\la $ is a real parameter, $s \\in (0,1)$, $n >2s$ and $2^*_{\\mu,s}= (2n-\\mu)/(n-2s)$ is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. We obtain some existence, multiplicity, regularity and nonexistence results for solution of the abo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06805","kind":"arxiv","version":2},"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"}