Re: Help: Loca stability for Lipshitz continuous ODE

From: Alwyn C. Scott (rover_at_theriver.com)
Date: 10/16/04

  • Next message: Mark Burke: "Re: Help: Loca stability for Lipshitz continuous ODE" 
    Date: 16 Oct 2004 09:53:31 -0700

    "Fan Yang" <yang@cae.wisc.edu> wrote in message news:<ckor63$425$1@news.doit.wisc.edu>...
    > Suppose we have an ODE system, x belongs to R^n,
    >
    > dx/dt = f(x), f: R^n -> R^n, Lipschitz continuous but
    > not continuously differentiable, for example, f(x) looks
    > like f(x) = g(max{x,0}) where g: R^n -> R^n is continuously
    > differentiable.
    >
    > Suppose p is a fixed point of the ODE system. How can
    > we analyze the local stability around fixed point p under the
    > above assumptions? Can anyone refer me a good book or
    > paper about this?
    >
    > Thanks a lot,
    >
    > Fan

    ===
    ===

    Dear Fan,

    I suggest that you look at the book "Stability By Liapunov's Direct
    Method, With Applications" by Joseph La Salle And Solomon Lefschetz. 

    Best wishes,

    Alwyn Scott
    http://personal.riverusers.com/~rover/

  • Next message: Mark Burke: "Re: Help: Loca stability for Lipshitz continuous ODE"