Does differential equation always has solution if vector field is only continuous? [duplicate]

Let $V$ be a $continuous$ vector-field defined on a domain $U$ in $R^n$ . Let $x_0$ be a point in $U$. Is it true that the differential equation $\frac{dx}{dt}$ = $V(x)$ admits a solution $\phi(t)$ satisfying initial condition $\phi(0)$=$x_0$ defined on some open interval containing $0$.

By Arnold's Book Existence theorem I know that unique solution exists in case of smooth vector field.But here vector field is only $continuous$.Can we have counterexample in this case?