Slow divergence integrals in generalized Lienard equations near centers

被引：0
|
作者：
Huzak, Renato [1 ]
De Maesschalck, Peter [1 ]
机构：
[1] Hasselt Univ, B-3590 Diepenbeek, Belgium
来源：
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2014年 / 66期
关键词：
generalized Lienard equations; limit cycles; slow divergence integral; slow-fast systems; LIMIT-CYCLE BIFURCATIONS; HILBERTS 16TH PROBLEM; DIFFERENTIAL-EQUATIONS; CUSPIDAL LOOP; SYSTEMS; UNIQUENESS; NUMBER;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Using techniques from singular perturbations we show that for any n >= 6 and m >= 2 there are Lienard equations {x = y - F(x), y = G ( x)}, with F a polynomial of degree n and G a polynomial of degree m, having at least 2[n-2/2] + [m/2] hyperbolic limit cycles, where [center dot] denotes "the greatest integer equal or below".
引用
收藏
页码：1 / 10
页数：10
相关论文
共 50 条
  • [31] OSCILLATION ANALYSIS OF CONFORMABLE FRACTIONAL GENERALIZED LIENARD EQUATIONS
    Can, Engin
    Adiguzel, Hakan
    [J]. THERMAL SCIENCE, 2022, 26 : S647 - S655
  • [32] EXISTENCE OF PERIODIC SOLUTION FOR PERTURBED GENERALIZED LIENARD EQUATIONS
    Boussaada, Islam
    Chouikha, A. Raouf
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2006,
  • [33] OSCILLATION ANALYSIS OF CONFORMABLE FRACTIONAL GENERALIZED LIENARD EQUATIONS
    Can, Engin
    Adiguzel, Hakan
    [J]. THERMAL SCIENCE, 2022, 26 (SpecialIssue2): : S647 - S655
  • [34] Pseudo-Abelian integrals and divergence integrals on slow-fast model system
    Bobienski, Marcin
    Nagrodzki, Michal
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2024, 192
  • [35] Darbouxian integrals for generalized Raychaudhuri equations
    Valls, Claudia
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2011, 52 (03)
  • [36] Generalized elliptic integrals and modular equations
    Anderson, GD
    Qiu, SL
    Vamanamurthy, MK
    Vuorinen, M
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 2000, 192 (01) : 1 - 37
  • [37] Centers and generalized centers of near-rings
    Cannon, G. Alan
    Farag, Mark
    Kabza, Lucyna
    [J]. COMMUNICATIONS IN ALGEBRA, 2007, 35 (02) : 443 - 453
  • [38] Centers and generalized centers of near-rings
    Farag, Mark
    Neuerburg, Kent M.
    [J]. NEARRINGS, NEARFIELDS AND RELATED TOPICS, 2017, : 80 - 90
  • [39] LIMIT CYCLES FOR DISCONTINUOUS GENERALIZED LIENARD POLYNOMIAL DIFFERENTIAL EQUATIONS
    Llibre, Jaume
    Mereu, Ana Cristina
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
  • [40] Existence and uniqueness of limit cycles for generalized φ-Laplacian Lienard equations
    Perez-Gonzalez, S.
    Torregrosa, J.
    Torres, P. J.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 439 (02) : 745 - 765
12345