{"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 $t\\in \\mathbb{R}$, $W\\in C^1(\\mathbb{R} \\times \\mathbb{R}^n,\\mathbb{R})$. Assuming that $L(t)$ is a positive semi-definite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09300","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"}