{"paper":{"title":"The universal bound property for a class of second order ODEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Alain Haraux (LJLL), Mama Abdelli","submitted_at":"2018-11-06T08:04:42Z","abstract_excerpt":"We consider the scalar second order ODE u + |u | $\\alpha$ u + |u| $\\beta$ u = 0, where $\\alpha$, $\\beta$ are two positive numbers and the non-linear semi-group S(t) generated on IR 2 by the system in (u, u). We prove that S(t)IR 2 is bounded for all t > 0 whenever 0 < $\\alpha$ < $\\beta$ and moreover there is a constant C independent of the initial data such that $\\forall$t > 0, u (t) 2 + |u(t)| $\\beta$+2 $\\le$ C max{t -- 2 $\\alpha$ , t -- ($\\alpha$+1)($\\beta$+2) $\\beta$--$\\alpha$ }."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02212","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"}