Changjian Liu
Soochow University (Suzhou)
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Publication
Featured researches published by Changjian Liu.
Nonlinearity | 2012
Changjian Liu; Guoting Chen; Jiazhong Yang
In this paper we study hyperelliptic limit cycles of the Lienard systems where, respectively, fm(x) and gn(x) are polynomials of degree m and n, gn(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.
Transactions of the American Mathematical Society | 2013
Changjian Liu; Dongmei Xiao
In this paper, we study the monotonicity of the ratio of two Abelian integrals
Nonlinearity | 2012
Changjian Liu
We study the cyclicity of period annuli of some reversible non-Hamiltonian quadratic systems under quadratic perturbations. In general, the first integral, which we study, is non-algebraic. Via estimating the number of zeros of the associated Abelian integral (first order Melnikov function), we show that the cyclicity is 2.
Journal of Differential Equations | 2009
Chengzhi Li; Changjian Liu; Jiazhong Yang
Journal of Mathematical Analysis and Applications | 2012
Changjian Liu; Guoting Chen; Guanrong Chen
Journal of Differential Equations | 2012
Changjian Liu
Journal of Differential Equations | 2010
Armengol Gasull; Changjian Liu; Jiazhong Yang
Journal of Mathematical Analysis and Applications | 2015
Shimin Li; Changjian Liu
Journal of Mathematical Analysis and Applications | 2013
Liqin Zhao; Minghui Qi; Changjian Liu
Comptes Rendus Mathematique | 2013
Guoting Chen; Tiecheng Li; Changjian Liu