
Lipschitz condition
Hi Guys,
I'm trying to get my head around this whole Lipschitz condition business, and while I understand the principle, I'm having trouble understanding it mathematically. I have the example IVP:
y'(t) = t*sqrt(y)
Which with y(0) = 0, fails on IVP solvers. Apparently this can be explained in terms of a Lipschitz condition, but I haven't got a clue where to start proving it.
Any help would be greatly appreciated.
Thanks!

If we write the DE as...
$\displaystyle y^{'} = f(t,y)$ (1)
... we observe that for $\displaystyle y=0$ the partial derivative $\displaystyle f_{y}$ has a singularity and the the Lipschitz aren't satisfied. As consequence of that the IVP...
$\displaystyle y^{'} = t\cdot \sqrt{y}$ , $\displaystyle y(0)=0$ (2)
... has more that one solution, among them $\displaystyle y= \frac{t^{4}}{16}$ and $\displaystyle y = 0$...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$