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We prove that such solutions have the limit profile of a \"tower of bubbles\", as $ \\varepsilon \\to 0^+$, i.e. the po"},"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":"1904.02738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-04T18:24:14Z","cross_cats_sorted":[],"title_canon_sha256":"63b8f0a11e29943dbcaa10b46455719fdb2607ca92a5e385f6f9dde61ee70560","abstract_canon_sha256":"0784090559f3d24c5c5e24ef3fdf304b65f857d53a3e63cdde52cf04c1665913"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:19.830523Z","signature_b64":"/zggfYEkTIEZXF7/CXuc78MoW1f3q0PeL+pHuRZ0V5irHmMU3JusukBhkXCrc9+thOuEUy5zQq28Kx0W+QVdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"163f06286e25af73006e30e6c7338b23cbb0dd8cd2457bdb1ceceba6eb5e509b","last_reissued_at":"2026-05-17T23:49:19.829986Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:19.829986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sign-changing bubble-tower solutions to fractional semilinear elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Iacopetti, Gabriele Cora","submitted_at":"2019-04-04T18:24:14Z","abstract_excerpt":"We study the asymptotic and qualitative properties of least energy radial sign-changing solutions to fractional semilinear elliptic problems of the form \\[ \\begin{cases} (-\\Delta)^s u = |u|^{2^*_s-2-\\varepsilon}u &\\text{in } B_R, \\\\ u = 0 &\\text{in }\\mathbb{R}^n \\setminus B_R, \\end{cases} \\] where $s \\in (0,1)$, $(-\\Delta)^s$ is the s-Laplacian, $B_R$ is a ball of $\\mathbb{R}^n$, $2^*_s := \\frac{2n}{n-2s}$ is the critical Sobolev exponent and $\\varepsilon>0$ is a small parameter. 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