{"paper":{"title":"Boundedness of semilinear Duffing equations at resonance with oscillating nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daxiong Piao, Yiqian Wang, Zhiguo Wang","submitted_at":"2013-12-06T12:29:52Z","abstract_excerpt":"In this paper, we prove the boundedness of all the solutions for the equation $\\ddot{x}+n^2x+g(x)+\\psi'(x)=p(t)$ with the Lazer-Leach condition on $g$ and $p$, where $n\\in \\mathbb{N^+}$, $p(t)$ and $\\psi'(x)$ are periodic and $g(x)$ is bounded. For the critical situation that $\\big |\\int_0^{2\\pi}p(t)e^{int}dt \\big|=2\\big|g(+\\infty)-g(-\\infty)\\big|$, we also prove a sufficient and necessary condition for the boundedness if $\\psi'(x)\\equiv0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1842","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"}