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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.1646","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-07T03:42:08Z","cross_cats_sorted":[],"title_canon_sha256":"9e836b717ace08991d9698c7a0247576c55ec5d485615d261312ec3208eb0cf1","abstract_canon_sha256":"b12db9af11eca0b963fcc4fe9bea7b1a0201f625a5e6619d5150f28508c94d52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:11.108380Z","signature_b64":"zg05TBZAjztnKdZ2wo+Yja7rbeLuGlUNDATq0C+TBu3QM8Zjl7S36G/yKhZ+HcTl1kMmcmlrh+hcAJobU9g/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2abc6de621a1bb0d9d113f95aba1d0ad5d6b06550dd44e04dc2b508ee78198d","last_reissued_at":"2026-05-18T01:10:11.107963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:11.107963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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