Article ID Journal Published Year Pages File Type
4616830 Journal of Mathematical Analysis and Applications 2013 17 Pages PDF
Abstract

In this paper, we prove that the cyclicity of period annuli for system dxdt=y,dydt=−(ax+bx3+cx5) under perturbations of polynomials with degree nn is not more than 54n−1354n−13 (taking into account the multiplicity), where a,b,c∈Ra,b,c∈R with c≠0c≠0 such that the unperturbed systems have at least one center.

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Physical Sciences and Engineering Mathematics Analysis
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