{"paper":{"title":"On the existence of homoclinic type solutions of inhomogenous Lagrangian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA","math.SG"],"primary_cat":"math.DS","authors_text":"Jakub Ciesielski, Joanna Janczewska, Nils Waterstraat","submitted_at":"2017-02-04T21:13:13Z","abstract_excerpt":"We study the existence of homoclinic type solutions for second order Lagrangian systems of the type $\\ddot{q}(t)-q(t)+a(t)\\nabla G(q(t))=f(t)$, where $t\\in\\mathbb{R}$, $q\\in\\mathbb{R}^n$, $a\\colon\\mathbb{R}\\to\\mathbb{R}$ is a continuous positive bounded function, $G\\colon\\mathbb{R}^n\\to\\mathbb{R}$ is a $C^1$-smooth potential satisfying the Ambrosetti-Rabinowitz superquadratic growth condition and $f\\colon\\mathbb{R}\\to\\mathbb{R}^n$ is a continuous bounded square integrable forcing term. A homoclinic type solution is obtained as limit of $2k$-periodic solutions of an approximative sequence of se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01346","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"}