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19 p, 397.8 KB Vector fields with homogeneous nonlinearities and many limit cycles / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yu, Jiang (Shanghai Jiao Tong University. Department of Mathematics) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
Consider planar real polynomial differential equations of the form x'=Lx X_n(x), where x=(x,y) R^2, L is a 2×2 matrix and X_n is a homogeneous vector field of degree n > 1. Most known results about these equations, valid for infinitely many n, deal with the case where the origin is a focus or a node and give either non-existence of limit cycles or upper bounds of one or two limit cycles surrounding the origin. [...]
2015 - 10.1016/j.jde.2015.01.009
Journal of differential equations, Vol. 258 (2015) , p. 3286-3303  

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