New lower bounds for the Hilbert number of polynomial systems of Liénard type

In this paper, we study the maximal number of limit cycles of some kinds of polynomial Liénard systems with arbitrary degree and obtain some new lower bounds for the Hilbert number of the systems, which improve truly the certain existing results.

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Bibliographic Details
Published inJournal of Differential Equations Vol. 257; no. 7; pp. 2565 - 2590
Main Authors Xiong, Yanqin, Han, Maoan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2014
Subjects
Elementary center
Hilbert number
Liénard system
Melnikov function
34C05
Hilbert number
Melnikov function
Elementary center
Liénard system
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Summary:In this paper, we study the maximal number of limit cycles of some kinds of polynomial Liénard systems with arbitrary degree and obtain some new lower bounds for the Hilbert number of the systems, which improve truly the certain existing results.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2014.05.058