On the rational solutions of generalized Abel equations

We study the nonconstant rational solutions of generalized Abel equations \[ x'=\sum_{i=1}^s A_i(t)x^{n_i},\qquad s\geq3,\qquad 1\leq n_1<\cdots<n_s, \] with polynomial coefficients over $\mathbb{R}$ or $\mathbb{C}$. Using the Newton diagram at infinity and the associated edge polynomials, we obtain