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We construct solutions of $P_\\epsilon$ which blow up and concentrate at strict local maximum of $K$ either at the boundary or in the interior of $\\Omega$. We also construct solutions of $P_\\epsilon$ concentrating at an interior strict local minimum of $K$. Finally, we prove a no"},"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":"math/0408352","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2004-08-25T15:46:21Z","cross_cats_sorted":[],"title_canon_sha256":"2a9b5e895c9c5c549af89e2297372a1fd754af8742c76372a7fd3d350d30e879","abstract_canon_sha256":"119237d166d5340d5b8440db6fd009fc7fffb881ba517ba5cbe9f847cb859e0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:26.051453Z","signature_b64":"2qrHCwYuTqvs4KlYeVw/kFdsmRb3bj1rVXqINz9xDgfFDDnm+lXChfInaTXXbyrYT3BcxqFoiUvl2ag6RdfhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"221055ce364f50328b97c77b65568f05e06298c6cf8605cc400492ce0e315608","last_reissued_at":"2026-05-18T01:05:26.050900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:26.050900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blowing up Solutions for a Biharmonic Equation with Critical Nonlinearity","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Khalil El Mehdi, Mokhless Hammami","submitted_at":"2004-08-25T15:46:21Z","abstract_excerpt":"In this paper we consider the following biharmonic equation with critical exponent $P_\\epsilon$ : $\\Delta^2 u= Ku^{(n+4)/(n-4)-\\epsilon}, u>0$ in $\\Omega$ and $u=\\Delta u=0$ on $\\partial\\Omega$, where $\\Omega$ is a domain in $R^n$, $n\\geq 5$, $\\epsilon$ is a small positive parameter and $K$ is smooth positive function. We construct solutions of $P_\\epsilon$ which blow up and concentrate at strict local maximum of $K$ either at the boundary or in the interior of $\\Omega$. We also construct solutions of $P_\\epsilon$ concentrating at an interior strict local minimum of $K$. 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