论文标题
具有全球中心的广义多项式系统的充分和必要条件
A sufficient and necessary condition of generalized polynomial Liénard systems with global centers
论文作者
论文摘要
本文的目的是提供具有全球中心的广义多项式Liénard系统的足够和必要的条件（包括线性的Typer和Nilpotent类型）。最近，Llibre和Valls [J。微分方程，330（2022），66-80]具有具有线性类型全球中心的广义多项式Liénard系统的足够且必要的条件。相比之下，很容易看出，我们足够和必要的条件更容易。特别是，我们提供了所有具有全球中心的全球多项式差异系统的明确表达，并且具有本质上具有全球中心的全球多项式差异化系统的显式表达。
The aim of this paper is to give a sufficient and necessary condition of the generalized polynomial Liénard system with a global center (including linear typer and nilpotent type). Recently, Llibre and Valls [J. Differential Equations, 330 (2022), 66-80] gave a sufficient and necessary condition of the generalized polynomial Liénard system with a linear type global center. It is easy to see that our sufficient and necessary condition is more easy by comparison. In particular, we provide the explicit expressions of all the generalized polynomial Liénard differential systems of degree 5 having a global center at the origin and the explicit expression of a generalized polynomial Liénard differential system of indefinite degree having a global center at the origin.
