A new uniqueness criterion for the number of periodic orbits of Abel equations

M. J. Alvarez, A. Gasull, H. Giacomini

A solution of the Abel equation $\dot{x}=A(t)x^3+B(t)x^2$ such that $x(0)=x(1)$ is called a periodic orbit of the equation. Our main result proves that if there exist two real numb…