{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:X7XI263PQGFLPT3W7BAWU2T6AX","short_pith_number":"pith:X7XI263P","schema_version":"1.0","canonical_sha256":"bfee8d7b6f818ab7cf76f8416a6a7e05cdc55ca9a2cdf7557b7d7a9fdf13b4d4","source":{"kind":"arxiv","id":"1709.03315","version":1},"attestation_state":"computed","paper":{"title":"Quasi-radial nodal solutions for the Lane-Emden problem in the ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Gladiali, Isabella Ianni","submitted_at":"2017-09-11T10:03:25Z","abstract_excerpt":"We consider the semilinear elliptic problem \\begin{equation}\\label{problemAbstract} \\left\\{\\begin{array}{lr}-\\Delta u= |u|^{p-1}u\\qquad \\mbox{ in }B\\\\ u=0\\qquad\\qquad\\qquad\\mbox{ on }\\partial B \\end{array}\\right.\\tag{$\\mathcal E_p$} \\end{equation} where $B$ is the unit ball of $\\mathbb R^2$ centered at the origin and $p\\in (1,+\\infty)$. We prove the existence of non-radial sign-changing solutions to \\eqref{problemAbstract} which are \\emph{quasi-radial}, namely solutions whose nodal line is the union of a finite number of disjoint simple closed curves, which are the boundary of nested domains c"},"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":"1709.03315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-11T10:03:25Z","cross_cats_sorted":[],"title_canon_sha256":"c167b693373ac448f1129df986a0128372a0c49a87efe0508821f0f850d5bf63","abstract_canon_sha256":"a6bf02c18ad353c4774b5851e1d07824d9661f07da3f581156dddb2ac0257bef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:38.767509Z","signature_b64":"jkE3SWcVLgFB0A0tUtjMiP0+BVHDwbuFfgW9oHSk/8AXCn0LrGcXSz5o8vUwiTQPkuLx7rirt1dl6VN5bW3zDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfee8d7b6f818ab7cf76f8416a6a7e05cdc55ca9a2cdf7557b7d7a9fdf13b4d4","last_reissued_at":"2026-05-18T00:35:38.766979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:38.766979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-radial nodal solutions for the Lane-Emden problem in the ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Gladiali, Isabella Ianni","submitted_at":"2017-09-11T10:03:25Z","abstract_excerpt":"We consider the semilinear elliptic problem \\begin{equation}\\label{problemAbstract} \\left\\{\\begin{array}{lr}-\\Delta u= |u|^{p-1}u\\qquad \\mbox{ in }B\\\\ u=0\\qquad\\qquad\\qquad\\mbox{ on }\\partial B \\end{array}\\right.\\tag{$\\mathcal E_p$} \\end{equation} where $B$ is the unit ball of $\\mathbb R^2$ centered at the origin and $p\\in (1,+\\infty)$. We prove the existence of non-radial sign-changing solutions to \\eqref{problemAbstract} which are \\emph{quasi-radial}, namely solutions whose nodal line is the union of a finite number of disjoint simple closed curves, which are the boundary of nested domains c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03315","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":"1709.03315","created_at":"2026-05-18T00:35:38.767079+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.03315v1","created_at":"2026-05-18T00:35:38.767079+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03315","created_at":"2026-05-18T00:35:38.767079+00:00"},{"alias_kind":"pith_short_12","alias_value":"X7XI263PQGFL","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"X7XI263PQGFLPT3W","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"X7XI263P","created_at":"2026-05-18T12:31:53.515858+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/X7XI263PQGFLPT3W7BAWU2T6AX","json":"https://pith.science/pith/X7XI263PQGFLPT3W7BAWU2T6AX.json","graph_json":"https://pith.science/api/pith-number/X7XI263PQGFLPT3W7BAWU2T6AX/graph.json","events_json":"https://pith.science/api/pith-number/X7XI263PQGFLPT3W7BAWU2T6AX/events.json","paper":"https://pith.science/paper/X7XI263P"},"agent_actions":{"view_html":"https://pith.science/pith/X7XI263PQGFLPT3W7BAWU2T6AX","download_json":"https://pith.science/pith/X7XI263PQGFLPT3W7BAWU2T6AX.json","view_paper":"https://pith.science/paper/X7XI263P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.03315&json=true","fetch_graph":"https://pith.science/api/pith-number/X7XI263PQGFLPT3W7BAWU2T6AX/graph.json","fetch_events":"https://pith.science/api/pith-number/X7XI263PQGFLPT3W7BAWU2T6AX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X7XI263PQGFLPT3W7BAWU2T6AX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X7XI263PQGFLPT3W7BAWU2T6AX/action/storage_attestation","attest_author":"https://pith.science/pith/X7XI263PQGFLPT3W7BAWU2T6AX/action/author_attestation","sign_citation":"https://pith.science/pith/X7XI263PQGFLPT3W7BAWU2T6AX/action/citation_signature","submit_replication":"https://pith.science/pith/X7XI263PQGFLPT3W7BAWU2T6AX/action/replication_record"}},"created_at":"2026-05-18T00:35:38.767079+00:00","updated_at":"2026-05-18T00:35:38.767079+00:00"}