Abstract:In this paper we consider the limit cycles of the planar system d dt (x, y) = Xn + Xm,where Xn and Xm are quasi-homogeneous vector fields of degree n and m respectively. We prove that under a new hypothesis, the maximal number of limit cycles of the system is 1. We also show that our result can be applied to some systems when the previous results are invalid. The proof is based on the investigations for the Abel equation and the generalized-polar equation associated with the system, respectively. Usually these… Show more
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