I have a question about LaSalle's invariance principle in the following version, which is the one I have to work with:
Let $D⊂R^n$ be open and let $f:D->R^n$ with $f(0) = 0$ be locally Lipschitz-continuous in D and let $V\in C^1(D)$ be a Lyapunov-function for f. If M = {$0$} is the largest invariant Subset of N = {x ∈ D : V' = $0$}, then $0$ is asymptotically stable.
So, my question is: Is it necessary for the solution y to be y=$0$, or can y be any constant solution with f(y)=$0$ (which fulfills the other assumptions of the theorem), so that the asymptotical stability holds for y?