Characterization of the Existence of Non-trivial Limit Cycles for Generalized Abel Equations

Abstract

In this paper, we consider the family of generalized Abel equations of the form $$\begin{aligned} x'=A(t)x^m + B(t) x^n, \end{aligned}$$ where A, B are trigonometric polynomials and $$m,n\in \mathbb {N}$$ . We characterize the existence of non-trivial limit cycles in this family, in terms of the trigonometric monomials.