Abstract
We consider the class of polynomial differential equations ẋ = Pn(x, y)+Pn+m(x, y)+Pn+2m(x, y)+Pn+3m(x, y), ẏ = Qn(x, y)+Qn+m(x, y)+Qn+2m(x,y)+Qn+3m(x, y), for n,m ≥ 1 and where Pi and Qi are homogeneous polynomials of degree i. Inside this class we identify new subclasses of Darboux integrable systems. Moreover, under additional conditions such Darboux integrable systems can have at most three limit cycles. We provide the explicit expression of these limit cycles.
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Giné, J., Llibre, J. (2005). Darboux Integrability and Limit Cycles for a Class of Polynomial Differential Systems. In: Wang, D., Zheng, Z. (eds) Differential Equations with Symbolic Computation. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7429-2_4
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DOI: https://doi.org/10.1007/3-7643-7429-2_4
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