[M@gpie]

มีโจทย์มาปลุกกระทู้กันซักนิดครับ ผมดูแล้ว งงๆ เล็กน้อยเลยมาขอคำแนะนำ
A vector valued function of a vector $\dot{\mathbf{x}}$ is said to satisfy a Lipchitz condition with respect to $\mathbf{x}$ if there exists a $k$ such that \[ \| \mathbf{f}(\mathbf{x}_1) - \mathbf{f}(\mathbf{x}_2) \| \leq k \| \mathbf{x}_1 -\mathbf{x}_2 \| \]
for all $\mathbf{x}_1,\mathbf{x}_2$. Show that for a given $\mathbf{x}_0$ there is at most one solution of the nonlinear equation $\dot{\mathbf{x}}= \mathbf{f}(\mathbf{x}(t))$ passing through $\mathbf{x}_0$ if $\mathbf{f}$ satisfies a Lipshitz condition.