{"paper":{"title":"On a Poincar\\'e-Perron problem for high order differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H. Bustos, Manuel Pinto, P. Figueroa","submitted_at":"2021-11-10T00:27:57Z","abstract_excerpt":"We address asymptotic formulae for the classical Poincar\\'e-Perron problem of linear differential equations with almost constant coefficients in a half line $[t_0,+\\infty)$ for high order equation $n\\ge 5$ and some $t_0\\in\\mathbb{R}$. By using a scalar nonlinear differential equation of Riccati type of order $n-1$, we recover Poincar\\'e's and Perron's results and provide asymptotic formulae with the aid of Bell's polynomials. Furthermore, we obtain some weaker versions of Levinson, Hartman-Wintner and Harris-Lutz type Theorems without the usual diagonalization process. For an arbitrary $n\\ge 5"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.05467","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.05467/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}