{"paper":{"title":"Infinitely many homoclinic orbits for a class of superquadratic Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mohsen Timoumi","submitted_at":"2013-02-21T11:53:48Z","abstract_excerpt":"In this paper, we prove the existence of infinitely many homoclinic orbits for the first order Hamiltonian systems $J\\dot{x}-M(t)x+ R'(t,x)=0$, by the minimax methods in critical point theory, when $R(t,y)$ satisfies the superquadratic condition ${{R(t,x)}\\over{\\|x\\r|^{2}}}\\longrightarrow \\pm\\infty$ as $\\|x\\|\\longrightarrow\\infty$, uniformly in $t$, and need not satisfy the global Ambrosetti-Rabinowitz condition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5258","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"}