{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LXTKIGB3EBAX6KMPJZGIAG3AGD","short_pith_number":"pith:LXTKIGB3","schema_version":"1.0","canonical_sha256":"5de6a4183b20417f298f4e4c801b6030fc4098fb7d178cdba2c2d728d0707be6","source":{"kind":"arxiv","id":"1808.01850","version":1},"attestation_state":"computed","paper":{"title":"$(p,2)$-equations asymmetric at both zero and infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Du\\v{s}an D. Repov\\v{s}, Nikolaos S. Papageorgiou, Vicen\\c{t}iu D. R\\u{a}dulescu","submitted_at":"2018-08-06T12:34:48Z","abstract_excerpt":"We consider a $(p,2)$-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a $p$-Laplacian and a Laplacian with $p>2$. The reaction term is $(p-1)$-linear but exhibits asymmetric behaviour at $\\pm\\infty$ and at $0^{\\pm}$. Using variational tools, together with truncation and comparison techniques and Morse theory, we prove two multiplicity theorems, one of them providing sign information for all the solutions (positive, negative, nodal)."},"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":"1808.01850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-06T12:34:48Z","cross_cats_sorted":[],"title_canon_sha256":"213fd69bbb8f26d82c73c14f67042165f22f2fd0a924798b96a885481151fae0","abstract_canon_sha256":"86059a0166bd9b8aead7745eeb969f54f20230e4ecb914beab1106f4a86305b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:49.466556Z","signature_b64":"J2L8EWVK0CFhUp+/2fRfUBCJEN7JC/wt9H6pUasu/M+WhMd47YcT7g3vFPzIWRY7t7NODFN80zGnrD+/WdZ+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5de6a4183b20417f298f4e4c801b6030fc4098fb7d178cdba2c2d728d0707be6","last_reissued_at":"2026-05-18T00:08:49.466017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:49.466017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$(p,2)$-equations asymmetric at both zero and infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Du\\v{s}an D. Repov\\v{s}, Nikolaos S. Papageorgiou, Vicen\\c{t}iu D. R\\u{a}dulescu","submitted_at":"2018-08-06T12:34:48Z","abstract_excerpt":"We consider a $(p,2)$-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a $p$-Laplacian and a Laplacian with $p>2$. The reaction term is $(p-1)$-linear but exhibits asymmetric behaviour at $\\pm\\infty$ and at $0^{\\pm}$. Using variational tools, together with truncation and comparison techniques and Morse theory, we prove two multiplicity theorems, one of them providing sign information for all the solutions (positive, negative, nodal)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01850","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":"1808.01850","created_at":"2026-05-18T00:08:49.466098+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.01850v1","created_at":"2026-05-18T00:08:49.466098+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01850","created_at":"2026-05-18T00:08:49.466098+00:00"},{"alias_kind":"pith_short_12","alias_value":"LXTKIGB3EBAX","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LXTKIGB3EBAX6KMP","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LXTKIGB3","created_at":"2026-05-18T12:32:37.024351+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/LXTKIGB3EBAX6KMPJZGIAG3AGD","json":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD.json","graph_json":"https://pith.science/api/pith-number/LXTKIGB3EBAX6KMPJZGIAG3AGD/graph.json","events_json":"https://pith.science/api/pith-number/LXTKIGB3EBAX6KMPJZGIAG3AGD/events.json","paper":"https://pith.science/paper/LXTKIGB3"},"agent_actions":{"view_html":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD","download_json":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD.json","view_paper":"https://pith.science/paper/LXTKIGB3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.01850&json=true","fetch_graph":"https://pith.science/api/pith-number/LXTKIGB3EBAX6KMPJZGIAG3AGD/graph.json","fetch_events":"https://pith.science/api/pith-number/LXTKIGB3EBAX6KMPJZGIAG3AGD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/action/storage_attestation","attest_author":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/action/author_attestation","sign_citation":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/action/citation_signature","submit_replication":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/action/replication_record"}},"created_at":"2026-05-18T00:08:49.466098+00:00","updated_at":"2026-05-18T00:08:49.466098+00:00"}