The Period Function of Second Order Differential Equations
| dc.creator | Chouikha, A. Raouf | |
| dc.date | 2001-03-27 | |
| dc.date.accessioned | 2026-07-07T04:40:47Z | |
| dc.date.available | 2026-07-07T04:40:47Z | |
| dc.description | We interest in the behaviour of the period function for equations of the type $u'' + g(u) = 0$ and $u'' + f(u)u' + g(u) = 0$ with a center at the origin 0. $g$ is a function of class $C^k$. For the conservative case, if $k \geq 2$ one shows that the Opial criterion is the better one among those for which these the necessary condition $g''(0) = 0$ holds. In the case where $f$ is of class $C^1$ and $k \geq 3$, the Lienard equations $ u'' + f(u) u' + g(u) = 0$ may have a monotonic period function if $g'(0) g^{(3)}(0) - {5/3} {g''}^{2}(0) - {2/3} {f'}^{2}(0) g'(0) \neq 0$ in a neighborhood of 0. {\it Key Words and phrases:} period function, monotonicity, isochronicity, Lienard equation, polynomial systems. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0103180 | |
| dc.identifier | http://arxiv.org/abs/math/0103180 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61149 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34C25, 34C35 | |
| dc.title | The Period Function of Second Order Differential Equations | |
| dc.type | text |