Slow Divergence Integrals in Classical Li,nard Equations Near Centers

De Maesschalck Peter; Huzak Renato

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Slow Divergence Integrals in Classical Li,nard Equations Near Centers

机译：靠近中心的经典Li，nard方程的慢散度积分

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摘要

We significantly improve lower bounds for the number of limit cycles for polynomial classical Li,nard equations, aiming at stating lower bounds that are reasonable enough to be optimal. The techniques used are the notion of slow divergence integral from the geometric theory of planar slow-fast systems.

机译：我们显着改善了多项式经典Li，nard方程的极限环数的下界，旨在阐明合理的下界，以使其达到最佳。所使用的技术是来自平面慢-快系统的几何理论的慢散度积分概念。

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来源
《Journal of dynamics and differential equations》 |2015年第1期|177-185|共9页
作者
De Maesschalck Peter; Huzak Renato;
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作者单位

Hasselt Univ, B-3590 Diepenbeek, Belgium;

Hasselt Univ, B-3590 Diepenbeek, Belgium;

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原文格式 PDF
正文语种 eng
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关键词
Classical Lienard equations; Limit cycles; Singular perturbations; Slow-fast systems; Slow divergence integral;

机译：古典Lienard方程;极限环;奇摄动;慢速系统;慢发散积分;

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1. Slow divergence integrals in generalized Liénard equations near centers [J] . Huzak Renato, De Maesschalck Peter Electronic Journal of Qualitative Theory of Differential Equations . 2014,第94期

机译：中心附近的广义Liénard方程的慢散度积分
2. Slow divergence integral and its application to classical Lienard equations of degree 5 [J] . Li Chengzhi, Lu Kening Journal of Differential Equations . 2014,第12期

机译：慢散度积分及其在经典5度Lienard方程中的应用
3. Limit cycles in discontinuous classical Liénard equations [J] . Ricardo Miranda Martins, Ana Cristina Mereu Nonlinear analysis. Real world applications . 2014,第Null期

机译：不连续经典Liénard方程的极限环
4. Center manifold analysis of the delayed Liénard equation [C] . Siming Zhao, Kalmar-Nagy Tamas European Control Conference . 2009

机译：时滞Liénard方程的中心流形分析
5. Lineer Eliptik k?smi Diferensiyel Denklemlerde Integral operat?rler =Integral operators in linear elliptic partial differential equations [D] . Ya??z, ?brahim. 2021

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6. A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type [O] . Shiping Lu -1

机译：具有奇异斥力型Liénard方程周期解存在性的新结果
7. Slow divergence integrals in generalized Liénard equations near centers [O] . Renato Huzakb, Peter De Maesschalck 2014

机译：中心附近广义Liénard方程的慢发散积分
8. Integrals of periodic motion and periodic solutions for classical equations of relativistic string with masses at ends. I. Integrals of periodic motion [R] . Barbashov, B. M. 1996

机译：具有末端质量的相对论弦经典方程的周期运动积分和周期解。 I.周期运动的积分

Slow Divergence Integrals in Classical Li,nard Equations Near Centers

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