Limit cycles for planar differential systems with quasi-homogeneous nonlinearities

Abstract

In this paper we study the estimate for the limit cycles of the planar differential systems of (p,q)-quasi-homogeneous polynomials nonlinearities. We give a condition on the polynomials to let the system have at most two limit cycles by introducing a new form of transformation. The tool that we mainly use is generalized polar coordinates and a fact introduced by Gasull and Llibre in estimating the number of limit cycles. This is achieved by estimating the number of isolated periodic solutions of Abel equation.