On Moment Condition and Center Condition for Abel Equation

2017/08/02 by Anderson L. A. de Araujo, de Araujo, Anderson L. A., Abílio Lemos +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1708.01512

arXiv admin note: text overlap with arXiv:1707.02664

arxiv created 2017/08/02 · arxiv updated 2017/08/07

Abstract

In this paper we consider Abel equation x' = g(t)x²+f(t)x³, 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=∫_-1¹f(t)(G(t))^kdt=0,~~k=0,1,2, is satisfied where G(t)=∫_-1^tg(s)ds. Besides, we give partial a positive answer to a conjecture proposed by Y. Lijun and T. Yun in 2001.

Citations

• Conditions to the existence of center in planar systems and center for Abel equations

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