{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LXTKIGB3EBAX6KMPJZGIAG3AGD","short_pith_number":"pith:LXTKIGB3","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"},"canonical_sha256":"5de6a4183b20417f298f4e4c801b6030fc4098fb7d178cdba2c2d728d0707be6","source":{"kind":"arxiv","id":"1808.01850","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01850","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01850v1","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01850","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"LXTKIGB3EBAX","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LXTKIGB3EBAX6KMP","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LXTKIGB3","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LXTKIGB3EBAX6KMPJZGIAG3AGD","target":"record","payload":{"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"},"canonical_sha256":"5de6a4183b20417f298f4e4c801b6030fc4098fb7d178cdba2c2d728d0707be6","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"},"source_kind":"arxiv","source_id":"1808.01850","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e7gdyTxGSorwNzIiRIsufB44FSsx43ZMG0Q6gINkw2rFqcn9DbnELSETJRxDsHHbt5q/ZbLNxVtDxan1uv/JAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:35:09.276303Z"},"content_sha256":"a6b43ef28e565ce58330c0f7a0f1f9a48c7d16abc395ffa2efd4c71ca1bcbd66","schema_version":"1.0","event_id":"sha256:a6b43ef28e565ce58330c0f7a0f1f9a48c7d16abc395ffa2efd4c71ca1bcbd66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LXTKIGB3EBAX6KMPJZGIAG3AGD","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2vlYGY7ny6YVuIbm5di4PDtYxzZLoqPg3YpoEqExqQFtNYJMoXLCgZEr5LM+bos51PjzPUuWSIYFPMaCoWvYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:35:09.276954Z"},"content_sha256":"d9451dbb7eaa1274c1da9422a5df57459b90691e9b1a3bb71bfbf3e9a6887ec4","schema_version":"1.0","event_id":"sha256:d9451dbb7eaa1274c1da9422a5df57459b90691e9b1a3bb71bfbf3e9a6887ec4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/bundle.json","state_url":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T10:35:09Z","links":{"resolver":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD","bundle":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/bundle.json","state":"https://pith.science/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXTKIGB3EBAX6KMPJZGIAG3AGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LXTKIGB3EBAX6KMPJZGIAG3AGD","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":"86059a0166bd9b8aead7745eeb969f54f20230e4ecb914beab1106f4a86305b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-06T12:34:48Z","title_canon_sha256":"213fd69bbb8f26d82c73c14f67042165f22f2fd0a924798b96a885481151fae0"},"schema_version":"1.0","source":{"id":"1808.01850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01850","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01850v1","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01850","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"LXTKIGB3EBAX","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LXTKIGB3EBAX6KMP","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LXTKIGB3","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:d9451dbb7eaa1274c1da9422a5df57459b90691e9b1a3bb71bfbf3e9a6887ec4","target":"graph","created_at":"2026-05-18T00:08:49Z","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":"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).","authors_text":"Du\\v{s}an D. Repov\\v{s}, Nikolaos S. Papageorgiou, Vicen\\c{t}iu D. R\\u{a}dulescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-06T12:34:48Z","title":"$(p,2)$-equations asymmetric at both zero and infinity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01850","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:a6b43ef28e565ce58330c0f7a0f1f9a48c7d16abc395ffa2efd4c71ca1bcbd66","target":"record","created_at":"2026-05-18T00:08:49Z","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":"86059a0166bd9b8aead7745eeb969f54f20230e4ecb914beab1106f4a86305b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-06T12:34:48Z","title_canon_sha256":"213fd69bbb8f26d82c73c14f67042165f22f2fd0a924798b96a885481151fae0"},"schema_version":"1.0","source":{"id":"1808.01850","kind":"arxiv","version":1}},"canonical_sha256":"5de6a4183b20417f298f4e4c801b6030fc4098fb7d178cdba2c2d728d0707be6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5de6a4183b20417f298f4e4c801b6030fc4098fb7d178cdba2c2d728d0707be6","first_computed_at":"2026-05-18T00:08:49.466017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:49.466017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J2L8EWVK0CFhUp+/2fRfUBCJEN7JC/wt9H6pUasu/M+WhMd47YcT7g3vFPzIWRY7t7NODFN80zGnrD+/WdZ+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:49.466556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6b43ef28e565ce58330c0f7a0f1f9a48c7d16abc395ffa2efd4c71ca1bcbd66","sha256:d9451dbb7eaa1274c1da9422a5df57459b90691e9b1a3bb71bfbf3e9a6887ec4"],"state_sha256":"e56d8387f6332a821357aa70f6fefe873e0f41eab0216cd3280816960c66f0fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z189sIJj4lxA9DGTlzOOtkmrnhV0fCP9AwQN65ghAhlYfs+mjCdUNt+ESG+rRqyKpOWHz9aN11XrBUW7WmFbAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T10:35:09.280520Z","bundle_sha256":"fb39c9a7b58c2e5d3b05224a8d263aed94cde8331f5084dc2dbb48f980c4db1a"}}