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

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

Abel equations of the form $x^{\prime }(t)=f(t)x^3(t)+g(t)x^2(t)$, $t\in [-a,a]$, where $a>0$ is a constant, $f$ and $g$ are continuous functions, are of interest because of their close re…