Mathematics – Dynamical Systems
Scientific paper
2001-03-27
Mathematics
Dynamical Systems
25 pages
Scientific paper
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.
No associations
LandOfFree
The Period Function of Second Order Differential Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Period Function of Second Order Differential Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Period Function of Second Order Differential Equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-28434