$ and we can write for any $t \in [0, t ^{ \varepsilon}_0]$ $$\frac{{ \varepsilon}\frac{{ \mathrm{d}}|{ V ^\varepsilon }|}{{ \mathrm{d}}t }}{ { \varepsilon}A + (\alpha - \beta |{ V ^\varepsilon }(t) |^0 ) \;|{ V ^\varepsilon }(t) |}\geq \frac{\frac{{ \mathrm{d}}|{ V ^\varepsilon }|}{{ \mathrm{d}}t }}{{ a ^\varepsilon}(t, { X ^\varepsilon }(t)) \cdot \frac{{ V ^\varepsilon }(t)}{|{ V ^\varepsilon }(t)|} + \frac{0}{{ \varepsilon}}(\alpha - \beta |{ V ^\varepsilon }(t) |^0 ) \;|{ V ^\varepsilon }(t) |} = 0$$ since $