Now I have found an answer to my question:
http://archive.numdam.org/ARCHIVE/AFST/
AFST_1996_6_5_4/AFST_1996_6_5_4_577_0/
AFST_1996_6_5_4_577_0.pdf
or, rather, Bernis and Qwang have found an answer. However, my differential equation is only of first degree, like
\dot K(t) = F(K(t))...
Dear all,
If a differential equation is Lipschitz continuous, then the solution is unique. But what about the implication in the other direction? I know that uniqueness does not imply Lipschitz continuity. But is there a counterexample? A differential equation that is not L-continuous, still...