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Torres Ledesma, Ziheng Zhang","submitted_at":"2016-10-26T11:57:57Z","abstract_excerpt":"In this paper we are concerned with the existence of ground states solutions for the following fractional Hamiltonian systems $$ \\left\\{ \\begin{array}{ll} -_tD^\\alpha_\\infty(_{-\\infty}D^\\alpha_t u(t)) - \\lambda L(t)u(t)+\\nabla W(t,u(t))=0,\\\\[0.1cm] u \\in H^\\alpha (\\mathbb{R},\\mathbb{R}^n), \\end{array} \\right.\\qquad(\\hbox{FHS})_\\lambda$$ where $\\alpha\\in (1/2,1)$, $t\\in \\mathbb{R}$, $u\\in \\mathbb{R}^n$, $\\lambda>0$ is a parameter, $L\\in C(\\mathbb{R},\\mathbb{R}^{n^2})$ is a symmetric matrix for all $t\\in \\mathbb{R}$, $W\\in C^1(\\mathbb{R} \\times \\mathbb{R}^n,\\mathbb{R})$ and $\\nabla W(t,u)$ is th"},"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":"1610.08286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-26T11:57:57Z","cross_cats_sorted":[],"title_canon_sha256":"3a0699ee4ebf612f2c60c999ef5c5a1721ec437fb25d800791f86b06244ec3ad","abstract_canon_sha256":"fb6c411363b47566b3b149fa683cc0d4318431ff27040f11e3476728ff97cb2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:51.142453Z","signature_b64":"GiCSlacRKZURioke3ZEM8ycSe7/dpU2Cxw7/P76z9wki7azgqOADsIIwquEfIgasVY/Mjv6HSxDxFBx9UDyzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0d74a9594ab1581847de6308e2679cf4dd3feeead97da565932a42576d487d2","last_reissued_at":"2026-05-18T00:32:51.141673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:51.141673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration of ground state solution for a fractional Hamiltonian Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C\\'esar E. Torres Ledesma, Ziheng Zhang","submitted_at":"2016-10-26T11:57:57Z","abstract_excerpt":"In this paper we are concerned with the existence of ground states solutions for the following fractional Hamiltonian systems $$ \\left\\{ \\begin{array}{ll} -_tD^\\alpha_\\infty(_{-\\infty}D^\\alpha_t u(t)) - \\lambda L(t)u(t)+\\nabla W(t,u(t))=0,\\\\[0.1cm] u \\in H^\\alpha (\\mathbb{R},\\mathbb{R}^n), \\end{array} \\right.\\qquad(\\hbox{FHS})_\\lambda$$ where $\\alpha\\in (1/2,1)$, $t\\in \\mathbb{R}$, $u\\in \\mathbb{R}^n$, $\\lambda>0$ is a parameter, $L\\in C(\\mathbb{R},\\mathbb{R}^{n^2})$ is a symmetric matrix for all $t\\in \\mathbb{R}$, $W\\in C^1(\\mathbb{R} \\times \\mathbb{R}^n,\\mathbb{R})$ and $\\nabla W(t,u)$ is th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08286","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":"1610.08286","created_at":"2026-05-18T00:32:51.141803+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.08286v1","created_at":"2026-05-18T00:32:51.141803+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08286","created_at":"2026-05-18T00:32:51.141803+00:00"},{"alias_kind":"pith_short_12","alias_value":"4DLUVFMUVMKY","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4DLUVFMUVMKYDBD5","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4DLUVFMU","created_at":"2026-05-18T12:29:58.707656+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/4DLUVFMUVMKYDBD54YYI4JTZZ5","json":"https://pith.science/pith/4DLUVFMUVMKYDBD54YYI4JTZZ5.json","graph_json":"https://pith.science/api/pith-number/4DLUVFMUVMKYDBD54YYI4JTZZ5/graph.json","events_json":"https://pith.science/api/pith-number/4DLUVFMUVMKYDBD54YYI4JTZZ5/events.json","paper":"https://pith.science/paper/4DLUVFMU"},"agent_actions":{"view_html":"https://pith.science/pith/4DLUVFMUVMKYDBD54YYI4JTZZ5","download_json":"https://pith.science/pith/4DLUVFMUVMKYDBD54YYI4JTZZ5.json","view_paper":"https://pith.science/paper/4DLUVFMU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.08286&json=true","fetch_graph":"https://pith.science/api/pith-number/4DLUVFMUVMKYDBD54YYI4JTZZ5/graph.json","fetch_events":"https://pith.science/api/pith-number/4DLUVFMUVMKYDBD54YYI4JTZZ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4DLUVFMUVMKYDBD54YYI4JTZZ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4DLUVFMUVMKYDBD54YYI4JTZZ5/action/storage_attestation","attest_author":"https://pith.science/pith/4DLUVFMUVMKYDBD54YYI4JTZZ5/action/author_attestation","sign_citation":"https://pith.science/pith/4DLUVFMUVMKYDBD54YYI4JTZZ5/action/citation_signature","submit_replication":"https://pith.science/pith/4DLUVFMUVMKYDBD54YYI4JTZZ5/action/replication_record"}},"created_at":"2026-05-18T00:32:51.141803+00:00","updated_at":"2026-05-18T00:32:51.141803+00:00"}