Uniqueness of Limit Cycles for Abel Equations and Planar Systems

José Luis Bravo Trinidad, Renhao Tian, Yulin Zhao

We study positive limit cycles of the Abel equation $$\dot{x}=A(t)x^3+B(t)x^2,$$ where $A$ and $B$ are $2\pi$-periodic functions. By developing a half-period convexity method, we…