On Moment Condition and Center Condition for Abel Equation

Anderson L. A. de Araujo, Abílio Lemos, Alexandre M. Alves

In this paper we consider Abel equation $x^{\prime }=g(t)x^2+f(t)x^3$, where $f$ and $g$ are analytical functions. We proved that if the equation has a center at $x=0$, then the Moment Co…