{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ERZKS7Z46JRN5QHU673ZZGFDRX","short_pith_number":"pith:ERZKS7Z4","schema_version":"1.0","canonical_sha256":"2472a97f3cf262dec0f4f7f79c98a38de59166c8bfb8af0fb6d91be7ae14fdf1","source":{"kind":"arxiv","id":"1309.5755","version":1},"attestation_state":"computed","paper":{"title":"On the solutions of a singular elliptic equation concentrating on two orthogonal spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B.B.Manna, P.N.Srikanth","submitted_at":"2013-09-23T10:24:35Z","abstract_excerpt":"Let $A=\\{x\\in \\R^{2m} : 0< a< |x| <b\\}$ be an annulus. Consider the following singularly perturbed elliptic problem on $A$\n  \\begin{equation}\n  \\begin{array}{lll}\n  -\\eps^2{\\De u} + |x|^{\\eta}u = |x|^{\\eta}u^p, &\\mbox{\\qquad in} A \\notag u>0 &\\mbox{\\qquad in} A u = 0 &\\mbox{\\qquad on} \\partial A\n  \\end{array} %\\label{a1}\n  \\end{equation} $1<p<2^*-1$. We shall prove the existence of a positive solution $u_\\eps$ which concentrates on two different orthogonal spheres of dimension $(m-1)$ as $\\eps\\to 0$. We achieve this by studying a reduced problem on an annular domain in $\\R^{m+1}$ and analyzing"},"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":"1309.5755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-23T10:24:35Z","cross_cats_sorted":[],"title_canon_sha256":"7d755a50ce07c104b6600703c82a8791e72787c09ee3c18c0c6cd643ee547600","abstract_canon_sha256":"e54eeaa96c0d7068fa9b0a73c7a81326c294a6a6bef206a7b6448d3bec33696d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:34.273077Z","signature_b64":"XIScOwqw470Tuge+CKNBrBpZ7BRH0qYVTCP7VGG0EDf/CudW7LO/weXsw7wyHWeaWOonnsagysN+NUG7+VO2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2472a97f3cf262dec0f4f7f79c98a38de59166c8bfb8af0fb6d91be7ae14fdf1","last_reissued_at":"2026-05-18T03:12:34.272339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:34.272339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the solutions of a singular elliptic equation concentrating on two orthogonal spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B.B.Manna, P.N.Srikanth","submitted_at":"2013-09-23T10:24:35Z","abstract_excerpt":"Let $A=\\{x\\in \\R^{2m} : 0< a< |x| <b\\}$ be an annulus. Consider the following singularly perturbed elliptic problem on $A$\n  \\begin{equation}\n  \\begin{array}{lll}\n  -\\eps^2{\\De u} + |x|^{\\eta}u = |x|^{\\eta}u^p, &\\mbox{\\qquad in} A \\notag u>0 &\\mbox{\\qquad in} A u = 0 &\\mbox{\\qquad on} \\partial A\n  \\end{array} %\\label{a1}\n  \\end{equation} $1<p<2^*-1$. We shall prove the existence of a positive solution $u_\\eps$ which concentrates on two different orthogonal spheres of dimension $(m-1)$ as $\\eps\\to 0$. We achieve this by studying a reduced problem on an annular domain in $\\R^{m+1}$ and analyzing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5755","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1309.5755","created_at":"2026-05-18T03:12:34.272522+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.5755v1","created_at":"2026-05-18T03:12:34.272522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5755","created_at":"2026-05-18T03:12:34.272522+00:00"},{"alias_kind":"pith_short_12","alias_value":"ERZKS7Z46JRN","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"ERZKS7Z46JRN5QHU","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"ERZKS7Z4","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ERZKS7Z46JRN5QHU673ZZGFDRX","json":"https://pith.science/pith/ERZKS7Z46JRN5QHU673ZZGFDRX.json","graph_json":"https://pith.science/api/pith-number/ERZKS7Z46JRN5QHU673ZZGFDRX/graph.json","events_json":"https://pith.science/api/pith-number/ERZKS7Z46JRN5QHU673ZZGFDRX/events.json","paper":"https://pith.science/paper/ERZKS7Z4"},"agent_actions":{"view_html":"https://pith.science/pith/ERZKS7Z46JRN5QHU673ZZGFDRX","download_json":"https://pith.science/pith/ERZKS7Z46JRN5QHU673ZZGFDRX.json","view_paper":"https://pith.science/paper/ERZKS7Z4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.5755&json=true","fetch_graph":"https://pith.science/api/pith-number/ERZKS7Z46JRN5QHU673ZZGFDRX/graph.json","fetch_events":"https://pith.science/api/pith-number/ERZKS7Z46JRN5QHU673ZZGFDRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ERZKS7Z46JRN5QHU673ZZGFDRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ERZKS7Z46JRN5QHU673ZZGFDRX/action/storage_attestation","attest_author":"https://pith.science/pith/ERZKS7Z46JRN5QHU673ZZGFDRX/action/author_attestation","sign_citation":"https://pith.science/pith/ERZKS7Z46JRN5QHU673ZZGFDRX/action/citation_signature","submit_replication":"https://pith.science/pith/ERZKS7Z46JRN5QHU673ZZGFDRX/action/replication_record"}},"created_at":"2026-05-18T03:12:34.272522+00:00","updated_at":"2026-05-18T03:12:34.272522+00:00"}