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We consider the Yamabe type problem \\begin{equation} \\left\\{ \\begin{array}{ll} -\\Delta_{g}u+au=0 & \\text{ on }M \\\\ \\partial_\\nu u+\\frac{n-2}{2}bu= u^{{n\\over n-2}\\pm\\varepsilon} & \\text{ on }\\partial M \\end{array}\\right. \\end{equation} where $a\\in C^1(M),$ $b\\in C^1(\\partial M)$, $\\nu$ is the outward pointing unit normal to $\\partial M $ and $\\varepsilon$ is a small positive parameter. We build solutions which blow-up at a point of the boundary as $\\varepsilon$ goes to zero. The blowing-up behavior is ruled by the func"},"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":"1506.09105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-30T14:25:19Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"283d75982af0bbd1e5888345109756f936435b61d98439b738cf9acd6bbc491d","abstract_canon_sha256":"7bb3799cda08bb2a56f781ca3b830089136944dd40c12ceb3eaca3763df1dd1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:33.662621Z","signature_b64":"Q4AYU9X0E0uleX2MhaM34JlUaiT7REBJxqpDudRDwEhmZ4HWk/KTKxmwmRZm1dtsumuuIpsrNpiSByQdeBQIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"818632747f548843f98e01adc8ad02e11191b4e74e19598e623823e38a5eaf7b","last_reissued_at":"2026-05-18T01:37:33.662117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:33.662117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Yamabe type problems on Riemannian manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Anna Maria Micheletti, Marco Ghimenti","submitted_at":"2015-06-30T14:25:19Z","abstract_excerpt":"Let $(M,g)$ be a $n-$dimensional compact Riemannian manifold with boundary. We consider the Yamabe type problem \\begin{equation} \\left\\{ \\begin{array}{ll} -\\Delta_{g}u+au=0 & \\text{ on }M \\\\ \\partial_\\nu u+\\frac{n-2}{2}bu= u^{{n\\over n-2}\\pm\\varepsilon} & \\text{ on }\\partial M \\end{array}\\right. \\end{equation} where $a\\in C^1(M),$ $b\\in C^1(\\partial M)$, $\\nu$ is the outward pointing unit normal to $\\partial M $ and $\\varepsilon$ is a small positive parameter. We build solutions which blow-up at a point of the boundary as $\\varepsilon$ goes to zero. 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