A Chebyshev criterion for at most two non-zero limit cycles in Abel equations

Jianfeng Huang, Renhao Tian, Yulin Zhao

In this paper, we investigate the maximum number of limit cycles of the reduced Abel equation $\dot{x}=A(t)x^3+B(t)x^2$ on an interval $[0,T]$. The Smale-Pugh problem asks whet…