{"paper":{"title":"Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chungen Liu, Qingye Zhang","submitted_at":"2011-06-02T03:14:26Z","abstract_excerpt":"In this paper we study the existence and multiplicity of homoclinic solutions for the second order Hamiltonian system $\\ddot{u}-L(t)u(t)+W_u(t,u)=0$, $\\forall t\\in\\mathbb{R}$, by means of the minmax arguments in the critical point theory, where $L(t)$ is unnecessary uniformly positively definite for all $t\\in \\mathbb{R}$ and $W_u(t, u)$ sastisfies the asymptotically linear condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0361","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"}