How Do I prove that x(t,ô,ϵ) is continuous in (t,ô,ϵ)
If f $\in$ $C^{r}_{x}(D,R^{d})\, r\geq1$, then for any $(\tau ,
\epsilon)\, \in D$, there is a unique solution $x(t,\tau,\epsilon)$ of the
IVP and $x(t,\tau,\epsilon)$ is continuous in $(t,\tau,\epsilon)$ together
with first derivatives with respect to t, $\tau$ and all derivative with
respect to $\epsilon$ up through order r.
NB: (D is an open subset of $R \times R^{d}$) any ideas will be very
helpful. Thanks
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