On the center of the generalized Liénard system

Title:

On the center of the generalized Liénard system

Creator:

Zhao, Cheng-Dong and He, Qi-Min

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:187594e7-6748-4bd6-be78-d41a1b3075da
uuid:187594e7-6748-4bd6-be78-d41a1b3075da

Subject:

generalized Liénard system, local center, global center, the differetial inequality theorem, and the first approximation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper, we discuss the conditions for a center for the generalized Liénard system \[ \frac {{\rm d}x}{{\rm d}t}=\varphi (y)-F(x), \qquad \frac {{\rm d}y}{{\rm d}t}=-g(x), \] or \[ \frac {{\rm d}x}{{\rm d}t}=\psi (y), \qquad \frac {{\rm dy}}{{\rm d}t}= -f(x)h(y)-g(x), \] with $f(x)$, $g(x)$, $\varphi (y)$, $\psi (y)$, $h(y)\: \mathbb R\rightarrow \mathbb R$, $F(x)=\int _0^xf(x)\mathrm{d}x$, and $xg(x)>0$ for $x\ne 0$. By using a different technique, that is, by introducing auxiliary systems and using the differential inquality theorem, we are able to generalize and improve some results in [1], [2].

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

817-832

Source:

Czechoslovak Mathematical Journal | 2002 Volume:52 | Number:4

Harvested from:

CDK

Metadata only:

false