{"paper":{"title":"Coron problem for nonlocal equations invloving Choquard nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Divya Goel, K. Sreenadh, Vicentiu D. Radulescu","submitted_at":"2018-04-22T08:21:19Z","abstract_excerpt":"We study the problem \\[ -\\De u = \\left(\\int_{\\Om}\\frac{|u(y)|^{2^*_{\\mu}}}{|x-y|^{\\mu}}dy\\right)|u|^{2^*_{\\mu}-2}u, \\; \\text{in}\\; \\Om,\\quad\n  u = 0 \\; \\text{ on } \\pa \\Om , \\] where $\\Om$ is a smooth bounded domain in $\\mathbb{R}^N( N\\geq 3)$, $2^*_{\\mu}=\\frac{2N-\\mu}{N-2}$. we prove the existence of a positive solution of the above problem in an annular type domain when the inner hole is sufficiently small."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08084","kind":"arxiv","version":3},"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"}