  We introduce a new method of proving pathwise uniqueness, and we apply it to
the degenerate stochastic differential equation \[dX_t=|X_t|^{\alpha} dW_t,\]
where $W_t$ is a one-dimensional Brownian motion and $\alpha\in(0,1/2)$. Weak
uniqueness does not hold for the solution to this equation. If one restricts
attention, however, to those solutions that spend zero time at 0, then pathwise
uniqueness does hold and a strong solution exists. We also consider a class of
stochastic differential equations with reflection.
