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Assuming that $L(t)$ is a positive semi-definite"},"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":"1808.09300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-28T13:53:42Z","cross_cats_sorted":[],"title_canon_sha256":"7e010a32e22cca59d3f8caec25f9bf2ad8be7337fb72591c99e184b7b536e149","abstract_canon_sha256":"2628155a8ed067dd47564288e6ccc859bf7f3594cf2499c767a3d410b693511e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:01.775717Z","signature_b64":"virRkfspR08AeDte4o9Ch8EShrbkMz2qQG2hNNeqkarnVfZfW5lO6V1gPID4ZaGo+O5eyy947yIfijy/QU7pDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"773f32bfa68327976c382b04061cdc25efc13546971c42932e58995d5205e626","last_reissued_at":"2026-05-18T00:07:01.775052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:01.775052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and concentration of solution for a fractional Hamiltonian systems with positive semi-definite matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amado Mendez, C\\'esar Torres, Ziheng Zhang","submitted_at":"2018-08-28T13:53:42Z","abstract_excerpt":"We study the existence of solutions for the following fractional Hamiltonian systems $$ \\left\\{\n  \\begin{array}{ll}\n  - _tD^{\\alpha}_{\\infty}(_{-\\infty}D^{\\alpha}_{t}u(t))-\\lambda L(t)u(t)+\\nabla W(t,u(t))=0,\\\\[0.1cm]\n  u\\in H^{\\alpha}(\\mathbb{R},\\mathbb{R}^n),\n  \\end{array} \\right.\n  \\eqno(\\mbox{FHS})_\\lambda $$ 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 $t\\in \\mathbb{R}$, $W\\in C^1(\\mathbb{R} \\times \\mathbb{R}^n,\\mathbb{R})$. 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