  For $\alpha\in (0,1)$, we consider stochastic differential equations driven
by one-sided stable processes of order $\alpha$: \[dX_t= \phi(X_{t-})\ dZ_t.\]
We prove that pathwise uniqueness holds for this equation under the assumptions
that $\phi$ is continuous, non-decreasing and positive on $\R$. A
counterexample is given to show that the positivity of $\phi$ is crucial for
pathwise uniqueness to hold.
