Limit cycle's uniqueness for second order O.D.E.'s polynomial in $\dot x$

TL;DR

This paper establishes a uniqueness result for limit cycles in a class of second order polynomial ODEs, extending previous work by applying an extended Massera theorem.

Contribution

It introduces a new uniqueness theorem for limit cycles in second order polynomial ODEs, expanding upon earlier results with a generalized approach.

Findings

Proves limit cycle uniqueness for a broad class of second order polynomial ODEs.

Extends Massera's theorem to accommodate more general conditions.

Builds upon and generalizes previous results in the literature.

Abstract

We prove a uniqueness result for limit cycles of the second order ODE $\ddot x + \sum_{j=1}^{J}f_{j}(x)\dot x^{j} + g(x) = 0$. We extend a uniqueness result proved in \cite{CRV}. The main tool applied is an extension of Massera theorem proved in \cite{GS}.