{"paper":{"title":"Caffarelli-Kohn-Nirenberg type equations of fourth order with the critical exponent and Rellich potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mousomi Bhakta","submitted_at":"2014-03-07T03:42:08Z","abstract_excerpt":"We study the existence/nonexistence of positive solution of $$ {\\Delta^2u-\\mu\\frac{u}{|x|^4}=\\frac{|u|^{q_{\\beta}-2}u}{|x|^{\\beta}}\\quad\\textrm{in $\\Omega$,}} $$ when $\\Omega$ is a bounded domain and $N\\geq 5$, $q_{\\beta}=\\frac{2(N-\\beta)}{N-4}$, $0\\leq \\beta<4$ and $0\\leq\\mu<\\big(\\frac{N(N-4)}{4}\\big)^2$. We prove the nonexistence result when $\\Omega$ is an open subset of $\\mathbf R^N$ which is star shaped with respect to the origin. We also study the existence of positive solution in $\\Omega$ when $\\Omega$ is a bounded domain with non trivial topology and $\\beta=0$, $\\mu\\in(0,\\mu_0)$, for ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1646","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"}