Limit cycles for planar differential systems with quasi-homogeneous nonlinearities

Khalil I.T. Al-Dosary

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.

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How to Cite this Article:

Khalil I.T. Al-Dosary, Limit cycles for planar differential systems with quasi-homogeneous nonlinearities, Journal of Mathematical and Computational Science, Vol 9, No 3 (2019), 365-371

Copyright © 2019 Khalil I.T. Al-Dosary. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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