On the number of limit cycles of a class of polynomial systems of Lienard type

[摘要] In this paper we study a planar system of the form (x) over dot = p(k)(y), (y) over dot = -g(m)(x) - epsilon f(n)(x)y, where p(k)(y) is a polynomial of degree k in y, and f(n)(x), g(m)(x) are polynomials in x with degree of n and m, respectively. Let H(m, n, k) denote the maximal number of limit cycles having odd multiplicities of this system. We give some lower bounds of H(m, n, k). (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] Limit cycle;Abelian integral;Hamiltonian function;Hilbert number