{"paper":{"title":"On Moment Condition and Center Condition for Abel Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ab\\'ilio Lemos, Alexandre M. Alves, Anderson L. A. de Araujo","submitted_at":"2017-08-02T19:34:16Z","abstract_excerpt":"In this paper we consider Abel equation $x' = g(t)x^2+f(t)x^3$, where $f$ and $g$ are analytical functions. We proved that if the equation has a center at $x=0$, then the Moment Conditions, i. e., $m_k=\\int_{-1}^1f(t)(G(t))^kdt=0,~~k=0,1,2$, is satisfied where $G(t)=\\int_{-1}^tg(s)ds$. Besides, we give partial a positive answer to a conjecture proposed by Y. Lijun and T. Yun in 2001."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01512","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"}