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arXiv · 1708.01512

On Moment Condition and Center Condition for Abel Equation

Anderson L. A. de Araujo·Abílio Lemos·Alexandre M. Alves
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Abstract

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.

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BibTeXRIS

Anderson L. A. de Araujo, Abílio Lemos, Alexandre M. Alves. 2017-08-02. On Moment Condition and Center Condition for Abel Equation. https://arxiv.org/abs/1708.01512

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