- #1
fortune
- 4
- 0
Hi,
For a first order Diff Equa. x'=f(x,t) and the IC: x(0)=x_0.
with t from [0 to infinity)
If f(x,t) doesn't satisfy the Lipschitz condition, can I say for sure that there doesn't exist a global unique solution?
I think the answer is "no" but I am not sure. Can you all confirm?
Also, can I use the Lipschitz condition to check the existence of a local solution around the IC? I see somebody often check the continuity of f(x) and df(x)/dx around the IC. Is this equavilent to the Lipschitz?
Thanks
For a first order Diff Equa. x'=f(x,t) and the IC: x(0)=x_0.
with t from [0 to infinity)
If f(x,t) doesn't satisfy the Lipschitz condition, can I say for sure that there doesn't exist a global unique solution?
I think the answer is "no" but I am not sure. Can you all confirm?
Also, can I use the Lipschitz condition to check the existence of a local solution around the IC? I see somebody often check the continuity of f(x) and df(x)/dx around the IC. Is this equavilent to the Lipschitz?
Thanks