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We prove the existence of positive solutions of two different types: either each density concentrates around a di"},"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":"1610.07762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-25T07:39:29Z","cross_cats_sorted":[],"title_canon_sha256":"dc42badbb9cc1b5e3a569c8e4b8a408a49430c23b4ff9d847ffa94b2fec28925","abstract_canon_sha256":"0f58d4655f119f8872ccb811a1201b2e1a36742fc73a31187503c4e12fcfbcfd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:17.693798Z","signature_b64":"jcJp7N0VKu7ngQvd+EYWkPb5+oRPXvDhIajz3KqgZn5YhTRbOSIoo3yl78Aw8if75lyMo7yJFTa1S72Z17JsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7f2233913c4e675814173fb13b85691a158fbde5378662f362f2f9b5fa4626d","last_reissued_at":"2026-05-18T01:01:17.693140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:17.693140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Coron's problem for weakly coupled elliptic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Nicola Soave","submitted_at":"2016-10-25T07:39:29Z","abstract_excerpt":"We consider the following critical weakly coupled elliptic system \\[ \\begin{cases} -\\Delta u_i = \\mu_i |u_i|^{2^*-2}u_i + \\sum_{j \\neq i} \\beta_{ij} |u_j|^{\\frac{2^*}{2}} |u_i|^{\\frac{2^*-4}{2}} u_i & \\text{in $\\Omega_\\varepsilon$} u_i >0 & \\text{in $\\Omega_\\varepsilon$} u_i = 0 & \\text{on $\\partial \\Omega_\\varepsilon$},\\end{cases} \\qquad i =1,\\dots,m, \\] in a domain $\\Omega_\\varepsilon \\subset \\mathbb{R}^N$, $N=3,4$, with small shrinking holes as the parameter $\\varepsilon \\to 0$. 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