{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OOSEV7VGDUAW2I47J5C4ZS6NE4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"534572b634004510ba7495b6565c7e32bc79d20f6ac7250c8b98be213de12893","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-19T16:14:54Z","title_canon_sha256":"7283dd5aab3477642fbfd927ce3d02f880e0d5b0174ca52eccc15e6fa2bcdf35"},"schema_version":"1.0","source":{"id":"1812.08055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.08055","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.08055v1","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08055","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"pith_short_12","alias_value":"OOSEV7VGDUAW","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OOSEV7VGDUAW2I47","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OOSEV7VG","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:7c1e3040e4d6b69f00c1e53b4293e04e5716b1e488c5e9835a4e9d66ee25acee","target":"graph","created_at":"2026-05-17T23:57:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A homogeneous Dirichlet problem with $(p,q)$-Laplace differential operator and reaction given by a parametric $p$-convex term plus a $q$-concave one is investigated. A bifurcation-type result, describing changes in the set of positive solutions as the parameter $\\lambda>0$ varies, is proven. Since for every admissible $\\lambda$ the problem has a smallest positive solution $\\bar u_{\\lambda}$, both monotonicity and continuity of the map $ \\lambda \\mapsto \\bar u_{\\lambda}$ are studied.","authors_text":"Greta Marino, Nikolaos S. Papageorgiou, Salvatore A. Marano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-19T16:14:54Z","title":"On a Dirichlet problem with $(p,q)$-Laplacian and parametric concave-convex nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08055","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d0a6c0460fcdfa06e71f6459f4e2af36b4071694aa26107407fac427bce710cb","target":"record","created_at":"2026-05-17T23:57:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"534572b634004510ba7495b6565c7e32bc79d20f6ac7250c8b98be213de12893","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-19T16:14:54Z","title_canon_sha256":"7283dd5aab3477642fbfd927ce3d02f880e0d5b0174ca52eccc15e6fa2bcdf35"},"schema_version":"1.0","source":{"id":"1812.08055","kind":"arxiv","version":1}},"canonical_sha256":"73a44afea61d016d239f4f45cccbcd272376788f095a103ffb8525f29ae8f169","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73a44afea61d016d239f4f45cccbcd272376788f095a103ffb8525f29ae8f169","first_computed_at":"2026-05-17T23:57:55.006133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:55.006133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GHpR9uRxJAj1duJpnnO6z8qRJLlYHxzKRNs9LOUjIKWRXNKGxBd/LyoIdv0wh3JjUoAB3YZG67wSx8HLqw4XAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:55.006671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0a6c0460fcdfa06e71f6459f4e2af36b4071694aa26107407fac427bce710cb","sha256:7c1e3040e4d6b69f00c1e53b4293e04e5716b1e488c5e9835a4e9d66ee25acee"],"state_sha256":"e6c47c998ed4a9b65b4d9016c62c542025380d73885140959a08602f809a5d22"}