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	On the hyperelliptic limit cycles of Lienard systems
	Liu, Changjian ; Chen, Guoting ; Yang, Jiazhong
	2012
关键词	HILBERTS 16TH PROBLEM EQUATION CURVES
英文摘要	In this paper we study hyperelliptic limit cycles of the Lienard systems x = y, y = - f(m)(x) y - g(n)(x), where, respectively, f(m)(x) and g(n)(x) are polynomials of degree m and n, g(n)(0) = 0. We prove that, if m >= 5 and m + 1 < n < 2m, then there always exist Lienard systems of the above form such that they have a hyperelliptic limit cycle. This gives a positive answer to the open problem posed in the paper by Yu and Zhang (2011 J. Math. Anal. Appl. 376 535-9). By combining all the results obtained up to now, we in fact give a complete classification of the hyperelliptic limit cycles of the Lienard systems: Lienard systems of the above form have hyperelliptic limit cycles only in the following cases: (i) m = 2, 3 and m + 3 <= n; (ii) 4 <= m and m + 2 <= n.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000305484500004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Applied; Physics, Mathematical; SCI(E); 3; ARTICLE; 6; 1601-1611; 25
语种	英语
出处	SCI
出版者	nonlinearity
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/393239]
专题	数学科学学院
推荐引用方式 GB/T 7714	Liu, Changjian,Chen, Guoting,Yang, Jiazhong. On the hyperelliptic limit cycles of Lienard systems. 2012-01-01.

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