Rational limit cycles of Abel equations

Abstract

We deal with Abel equations $ dy/dx = A(x) y^2 + B(x) y^3 $, where $ A(x) $ and $ B(x) $ are real polynomials. We prove that these Abel equations can have at most two rational limit cycles and we characterize when this happens. Moreover we provide examples of these Abel equations with two nontrivial rational limit cycles.